Bounds on the minimum distance of additive quantum codes
Bounds on [[73,13]]2
lower bound: | 13 |
upper bound: | 21 |
Construction
Construction of a [[73,13,13]] quantum code:
[1]: [[65, 13, 13]] quantum code over GF(2^2)
cyclic code of length 65 with generating polynomial x^64 + x^63 + w*x^62 + w*x^61 + w^2*x^60 + w*x^59 + x^57 + x^55 + w^2*x^54 + w*x^53 + w*x^52 + w*x^51 + x^50 + w*x^49 + w^2*x^48 + x^47 + x^46 + x^45 + x^44 + w^2*x^43 + w*x^42 + x^41 + w*x^40 + w*x^39 + w*x^38 + w^2*x^37 + x^36 + x^34 + w*x^32 + w^2*x^31 + w*x^30 + w*x^29 + x^28 + x^27 + x^26 + 1
[2]: [[73, 13, 13]] quantum code over GF(2^2)
ExtendCode [1] by 8
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 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0|0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0|0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0|0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 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 0 0 0 0 0 0 0 0 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 0 0 0 1 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 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 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 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0|1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0|0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0|1 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 1 0 0 0 0 0 0 0 0|0 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0|0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 0 0 0 0 0 0 0 0|1 0 0 1 1 1 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 0 0 0 0 0 0 0|0 1 0 0 1 1 1 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 0 0 0 0 0 0|1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 0 0 0 0 0 0 0 0|1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 0 0 0 0 0 0 0|0 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 0 0 0 0 0 0 0|1 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 1 0 0 0 0 0 0 0 0|1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0|1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0|1 1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0|1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0 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 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0|1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 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 1 0 0 0 0 0 0 0 0 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 1 0 0 0 1 0 0 0 0 0 0 0 0|0 1 1 1 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 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 1 0 0 0 0 0 0 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 1 1 0 0 0 0 0 0 0 0 0|0 0 1 1 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 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 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 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0|1 0 0 1 1 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 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 1 0 0 0 0 0 0 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 1 0 1 1 0 0 0 0 0 0 0 0|1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 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 1 0 0 0 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 0 0 0 0 0 0 0 0|0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 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 1 0 0 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 1 1 1 1 1 0 0 0 0 0 0 0 0|1 0 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 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 1 0 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 0 0 0 0 1 0 0 0 0 0 0 0 0|0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 1 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 0 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 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0|1 0 1 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 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 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 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0|0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 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 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 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0|1 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 1 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 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 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0|0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 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 1 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 0 0 0 0 0 0 0 0|0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 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 1 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 0 0 0 0 0 0 0|1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 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 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 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0|0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 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 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 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0|1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 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 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 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0|0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 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 1 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 1 0 0 0 0 0 0 0 0 0|0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 1 1 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 1 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 1 0 0 0 0 0 0 0 0|1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 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 0 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 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0|0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0|0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0|1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 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 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0|0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 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 0 0 0 0 0 0 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 1 0 1 0 0 1 1 1 1 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 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 1 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0|1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0|0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0|0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 0 0 0 0 0 0 0 0 0|1 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 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 0 0 0 0 0 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 1 1 1 1 0 0 0 0 0 0 0 0|1 1 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 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 0 0 0 0 0 0 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 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0|0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 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 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 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0|0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0|0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 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 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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