Bounds on the minimum distance of additive quantum codes
Bounds on [[62,24]]2
lower bound: | 9 |
upper bound: | 14 |
Construction
Construction of a [[62,24,9]] quantum code:
[1]: [[63, 24, 10]] quantum code over GF(2^2)
cyclic code of length 63 with generating polynomials [
w*x^60 + w^2*x^59 + x^57 + w*x^56 + x^54 + w*x^53 + w^2*x^52 + w*x^50 + x^49 + w^2*x^48 + w^2*x^47 + w^2*x^46 + w*x^45 + x^44 + x^43 + w^2*x^42 + x^41 + w*x^39 + w*x^38 + w^2*x^36 + w*x^35 + w^2*x^34 + w^2*x^33 + x^32 + x^31 + w^2*x^30 + w^2*x^29 + w^2*x^26 + w^2*x^25 + w^2*x^24 + w^2*x^23 + w^2*x^21 + x^19 + 1,
x^61 + w*x^57 + w*x^56 + x^54 + w*x^53 + w^2*x^52 + w*x^51 + x^50 + w^2*x^49 + w^2*x^47 + x^46 + x^43 + w^2*x^42 + w^2*x^41 + w^2*x^40 + x^36 + w^2*x^35 + w*x^34 + x^33 + x^32 + x^31 + w^2*x^29 + w^2*x^28 + x^27 + x^26 + w*x^24 + w^2*x^23 + w^2*x^22 + w^2*x^21 + w*x^20 + x^19 + w
]
[2]: [[62, 24, 9]] quantum code over GF(2^2)
Puncturing of [1] at { 63 }
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 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 1 1 1 1 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 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 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 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 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 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 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 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 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 1 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 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 1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0 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 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 1 0 1 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 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 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 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 0 1 1 1 0 0 1 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 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 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 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 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 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 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 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 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 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 1 1 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 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 1 1 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 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 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 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 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 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 0 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 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 0 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 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 0 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 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 0 0 1 0 0 1 1 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 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 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 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1 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 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 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 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 1 1 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 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 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 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 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 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 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 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 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 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 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 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 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 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 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 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 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 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 0 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 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 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 0 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 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 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 0 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 1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1]
last modified: 2006-04-03
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 even 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.
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Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014