Bounds on the minimum distance of additive quantum codes
Bounds on [[83,29]]2
lower bound: | 11 |
upper bound: | 19 |
Construction
Construction of a [[83,29,11]] quantum code:
[1]: [[85, 29, 13]] quantum code over GF(2^2)
cyclic code of length 85 with generating polynomials [
w^2*x^81 + w^2*x^80 + x^79 + w^2*x^78 + x^77 + x^76 + w^2*x^75 + x^74 + w^2*x^71 + w*x^70 + x^68 + w^2*x^67 + x^66 + x^64 + w^2*x^63 + w*x^62 + w^2*x^61 + w^2*x^60 + x^59 + w*x^58 + x^57 + x^56 + x^55 + w*x^54 + w^2*x^53 + x^52 + w^2*x^51 + w*x^50 + w^2*x^49 + w*x^48 + w^2*x^47 + w*x^43 + w^2*x^41 + w^2*x^40 + w*x^39 + w^2*x^37 + x^36 + w*x^35 + x^33 + w^2*x^31 + w*x^30 + w^2*x^29 + x^28 + 1,
x^81 + x^80 + w*x^79 + x^78 + w*x^77 + w*x^76 + x^75 + w*x^74 + x^71 + w^2*x^70 + w*x^68 + x^67 + w*x^66 + w*x^64 + x^63 + w^2*x^62 + x^61 + x^60 + w*x^59 + w^2*x^58 + w*x^57 + w*x^56 + w*x^55 + w^2*x^54 + x^53 + w*x^52 + x^51 + w^2*x^50 + x^49 + w^2*x^48 + x^47 + w^2*x^43 + x^41 + x^40 + w^2*x^39 + x^37 + w*x^36 + w^2*x^35 + w*x^33 + x^31 + w^2*x^30 + x^29 + w*x^28 + w
]
[2]: [[83, 29, 11]] quantum code over GF(2^2)
Puncturing of [1] at { 84 .. 85 }
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 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1|0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 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 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0|0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 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 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1|0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 0 0 0 0 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 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 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 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1 0 1 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 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 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1|0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 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 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1|0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 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 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 1|0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1 0 1 1 0 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 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0|0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 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 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 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 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 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 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 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 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 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 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 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 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0|0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 0|0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 1 0 0 1 1 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 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1|0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 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 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 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 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 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 0 1 1 1|0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 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 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 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 0 1 1|0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0|0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 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 1 0 0 0 0 0 0 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 1 1 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 1|0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 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 1 0 0 0 0 0 0 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 1 1 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1|0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 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 1 0 0 0 0 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 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 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 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 1 0 0 0 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 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1|0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 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 1 0 0 0 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 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0|0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 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 1 0 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 1 0 0 1 1 0 0 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0|0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0 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 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 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 1|0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 0 1 1 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 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 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 1 1 0 1 1|0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 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 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 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0|0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 0 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 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 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0|0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 0 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 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 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1|0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 1 1 0 1 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 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 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0|0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 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 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 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0|0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 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 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 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 1|0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 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 1 0 0 0 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 1 1 0 1 0 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0|0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0 1 0 1 0 1 1|0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 0 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 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 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0|0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 1 1|0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 1|0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0|0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1|0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 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 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 0 1 1 1 1 0 1 1 0 0 1 0 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 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 0 1|0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 0 1 0 1 0 1 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 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 1 1 0 1|0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 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 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1|0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 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 0 0 0 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 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1|0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 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 0 0 0 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 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1|0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 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 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0|0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 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 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0|0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 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 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1|0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 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.
This page is maintained by
Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014