Bounds on the minimum distance of additive quantum codes
Bounds on [[78,4]]2
| lower bound: | 17 |
| upper bound: | 26 |
Construction
Construction type: EzermanGrasslLingOzbudakOzkaya
Construction of a [[78,4,17]] quantum code:
[1]: [[78, 4, 17]] quantum code over GF(2^2)
QuasiCyclicCode of length 78 stacked to height 2 with generating polynomials: x^8 + w*x^7 + x^6 + x^5 + w*x^4 + w*x^3 + w^2*x^2 + w*x + w, w^2*x^32 + w^2*x^31 + x^30 + x^29 + w*x^28 + w^2*x^27 + w^2*x^26 + w^2*x^24 + w^2*x^23 + w^2*x^22 + w^2*x^21 + x^20 + w*x^19 + x^18 + w^2*x^17 + x^16 + w*x^15 + w^2*x^14 + x^13 + x^12 + x^11 + w*x^10 + w^2*x^8 + w^2*x^7 + w*x^6 + w*x^5 + w^2*x^4 + w^2*x^3 + w*x^2 + x + w^2, 0, x^33 + w*x^32 + w^2*x^31 + w^2*x^30 + w*x^29 + w^2*x^28 + w^2*x^27 + w^2*x^26 + w^2*x^20 + x^19 + w*x^18 + w*x^17 + x^16 + w*x^15 + w*x^14 + w*x^13 + w*x^7 + w^2*x^6 + x^5 + x^4 + w^2*x^3 + x^2 + x + 1
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 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 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 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 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 0 0 0 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 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 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 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 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 0 1 0 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 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 1 1 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 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 1 1 0 1 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 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 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 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 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 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 0 1 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 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 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 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 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 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 0 1 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 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 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 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 1 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 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 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 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 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 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 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 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 1 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 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 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 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 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 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 1 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 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 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 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 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 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1 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 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 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 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 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 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 1 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 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 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 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 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 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 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 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 1 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 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 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 1 0 0 0 1 1 1 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 1 0 0 0 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 1 0 0 0 1 1 1 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 1 0 0 0 1 0 0 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 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 1 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 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 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 1 0 0 0 1 1 1 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 1 0 0 0 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 1 0 0 0 1 1 1 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 1 0 0 0 1 0 0 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 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 1 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 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 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 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 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 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 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 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 0 1 0 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 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 1 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 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 1 1 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 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 0 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 1 1 0 1 0 1 1 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 0 0 1 1 1 1 0 0 0 0 1 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 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 0 0 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 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 0 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 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 1 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 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 0 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 1 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 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 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 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 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 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1|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 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 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 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 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 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 1 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 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 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 1 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 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 1 1 0 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 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 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 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 0 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 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 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 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 1 1 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 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 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 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 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 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 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 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 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 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 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 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 0 0 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 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 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 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 0 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 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 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 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 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 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0 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 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 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 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 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 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 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 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 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 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 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 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 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 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 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 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 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 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 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 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 1 0 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 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 1 0 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 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 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 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 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 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 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 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 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 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 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 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 0 0 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 1 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 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 1 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 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 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 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 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 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 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 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 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 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 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 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 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 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 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 1 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 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 1 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 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 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 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 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 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 1 1 0 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 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 1 1 0 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 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 1 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 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 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 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 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 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 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 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 1 0 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 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 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 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 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 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 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 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 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 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 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 1 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 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 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 0 1 0 0 0 1 0 0 0 1 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 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 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 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 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 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 1 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 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 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 0 1 0 0 0 1 0 0 0 1 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 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 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 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 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 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 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 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 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 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 0 0 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 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 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 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 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 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 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 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 0 0 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 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 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 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 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 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 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 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 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 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