Bounds on the minimum distance of additive quantum codes
Bounds on [[96,0]]2
| lower bound: | 22 |
| upper bound: | 34 |
Construction
Construction type: EzermanGrasslLingOzbudakOzkaya
Construction of a [[96,0,22]] quantum code:
[1]: [94, 48] Quasicyclic of degree 2 Linear Code over GF(2^2)
QuasiCyclicCode of length 94 stacked to height 2 with generating polynomials: 1, x^45 + w*x^44 + w*x^41 + w^2*x^40 + w^2*x^39 + x^38 + w^2*x^36 + w*x^35 + x^33 + w*x^32 + x^31 + x^30 + w^2*x^29 + w*x^28 + w*x^27 + w*x^25 + x^23 + w*x^22 + w^2*x^21 + w^2*x^19 + w^2*x^15 + x^14 + w*x^13 + w^2*x^11 + x^9 + w^2*x^8 + x^6 + w*x^4 + x^3 + w^2, 0, x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1
[2]: [[96, 0, 22]] self-dual quantum code over GF(2^2)
QuantumConstructionX applied to [1] with e = 2
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1|1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0|0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0|0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 1]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1|0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0|0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0|0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1|0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 1|0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1|0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 0|0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1]
last modified: 2024-05-23
Notes
- All codes establishing the lower bounds where constructed using MAGMA.
- Most upper bounds on qubit codes for n≤100 are based on a MAGMA program by Eric Rains.
- For n>100, the upper bounds on qubit codes are weak (and not necessarily monotone in k).
- Some additional information can be found in the book by Nebe, Rains, and Sloane.
- My apologies to all authors that have contributed codes to this table for not giving specific credits.
This page is maintained by
Markus Grassl
(codes@codetables.de).
Last change: 10.06.2024