Bounds on the minimum distance of additive quantum codes
Bounds on [[99,26]]2
lower bound: | 14 |
upper bound: | 25 |
Construction
Construction of a [[99,26,14]] quantum code:
[1]: [[91, 25, 15]] quantum code over GF(2^2)
cyclic code of length 91 with generating polynomials [
w*x^89 + x^87 + w^2*x^85 + w*x^84 + w^2*x^83 + w*x^82 + w*x^80 + w^2*x^79 + w*x^78 + w*x^77 + w^2*x^76 + w*x^75 + w*x^74 + w*x^72 + x^71 + w*x^70 + w*x^69 + w*x^68 + w^2*x^66 + x^65 + x^63 + x^62 + w*x^61 + x^60 + x^59 + w^2*x^56 + x^55 + w^2*x^54 + w*x^53 + w*x^52 + w*x^51 + x^49 + x^48 + w^2*x^47 + w^2*x^45 + w^2*x^44 + w*x^42 + w^2*x^41 + w^2*x^40 + w^2*x^38 + w*x^36 + w^2*x^34 + x^33 + 1,
w^2*x^89 + w*x^87 + x^85 + w^2*x^84 + x^83 + w^2*x^82 + w^2*x^80 + x^79 + w^2*x^78 + w^2*x^77 + x^76 + w^2*x^75 + w^2*x^74 + w^2*x^72 + w*x^71 + w^2*x^70 + w^2*x^69 + w^2*x^68 + x^66 + w*x^65 + w*x^63 + w*x^62 + w^2*x^61 + w*x^60 + w*x^59 + x^56 + w*x^55 + x^54 + w^2*x^53 + w^2*x^52 + w^2*x^51 + w*x^49 + w*x^48 + x^47 + x^45 + x^44 + w^2*x^42 + x^41 + x^40 + x^38 + w^2*x^36 + x^34 + w*x^33 + w
]
[2]: [[90, 26, 14]] quantum code over GF(2^2)
Shortening of the stabilizer code of [1] at 91
[3]: [[99, 26, 14]] quantum code over GF(2^2)
ExtendCode [2] by 9
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 0 0 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 1 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 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 0 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 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 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 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 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 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 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 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 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 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 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 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 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 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 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 0 0 0 0 0 0 0 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 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 0 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 1 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 0 1 1 0 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 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 1 1 1 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 1 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 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 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 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 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 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 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 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 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 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 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 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 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 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 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 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 1 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 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 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 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 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 1 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 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 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 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 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 1 0 0 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 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 1 0 0 0 0 0 0 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 1 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 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 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 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 1 0 0 0 0 0 0 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 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 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 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 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 1 0 0 0 0 0 0 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 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 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 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 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 1 0 0 0 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 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 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 1 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 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 1 0 0 0 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 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 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 1 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 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 1 0 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 1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 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 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 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 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 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 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 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 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 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 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 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 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 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 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 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 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 0 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 1 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 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 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 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 1 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 0 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 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 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 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 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 1 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 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 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 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 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 0 0 0 0 0 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 1 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 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 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 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 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 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 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 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 0 1 0 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 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 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 1 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 1 1 1 1 0 1 0 1 0 1 0 0 1 0 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 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 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 1 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 1 1 1 1 0 1 0 1 0 1 0 0 1 0 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 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 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 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 1 1 1 1 0 1 0 1 0 1 0 0 1 0 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 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 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 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 1 1 1 1 0 1 0 1 0 1 0 0 1 0 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 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 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 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 1 1 1 1 0 1 0 1 0 1 0 0 1 0 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 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 0 1 0 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 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 0 0 1 0 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 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1 0 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 1 0 1 1 1 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 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 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1 0 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 1 0 1 1 1 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 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 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1 0 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 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1 0 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 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 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 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1 0 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 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 0 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 1 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 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 0 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 0 1 0 1 1 0 1 1 0 0 0 1 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 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 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 0 0 0 0 0 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 1 0 0 1 0 0 0 1 1 1 0 0 1 0 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 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 1 1 0 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 1 0 0 0 1 1 0 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0]
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