Bounds on the minimum distance of additive quantum codes
Bounds on [[92,40]]2
lower bound: | 11 |
upper bound: | 18 |
Construction
Construction of a [[92,40,11]] quantum code:
[1]: [[91, 43, 10]] quantum code over GF(2^2)
cyclic code of length 91 with generating polynomial w^2*x^90 + x^89 + w*x^88 + x^87 + w*x^86 + w*x^85 + w^2*x^84 + x^83 + w*x^82 + x^81 + w*x^80 + x^79 + x^78 + x^76 + w^2*x^75 + w^2*x^74 + w^2*x^73 + w^2*x^72 + x^70 + w^2*x^68 + w^2*x^67 + w^2*x^66 + w^2*x^64 + w*x^62 + x^61 + x^59 + w*x^56 + w*x^55 + x^54 + x^53 + x^52 + w*x^51 + w^2*x^49 + x^48 + w*x^47 + w^2*x^46 + w^2*x^44 + x^43 + x^42 + w*x^41 + w*x^40 + w^2*x^39 + w^2*x^38 + w^2*x^37 + w^2*x^36 + x^35 + w*x^34 + w*x^32 + x^31 + w*x^30 + w*x^29 + w*x^28 + w*x^27 + w^2*x^26 + x^24 + 1
[2]: [[92, 42, 11]] quantum code over GF(2^2)
standard lengthening of [1]
[3]: [[92, 40, 11]] quantum code over GF(2^2)
Subcode of [2]
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 1 0 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1|0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1 0 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 0 0 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 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 1 0|0 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 1 0 1 1 1 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 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 1 1 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 1 0|0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 0|0 1 1 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1|0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 1 0 1 0 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 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 0 1 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1 1 0|0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 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 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 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1|0 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 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 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1|0 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 1|0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 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 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 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 1 0|0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 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 0 0 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 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 1 0 0 1 0|0 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 0 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 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1|0 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 1 0 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 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 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0|0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 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 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0|0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 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 0 0 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 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 0 1|0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 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 1 0 1 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1|0 1 0 1 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 1 1|0 1 0 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 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 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0|0 1 1 1 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 1 1 1 1 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 1 0 0 0 0 0 0 0 0 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 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1|0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 0 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 0 1 0 0 0 0 0 0 0 0 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 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0|0 1 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 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 1 0 0 0 0 0 0 0 0 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 1 1 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0|0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 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 1 0 0 0 0 0 0 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 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 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 0 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 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 1 0 0 0 0 0 0 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 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1|0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 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 1 0 0 0 0 0 0 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 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1|0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 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 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 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 1 0 1 1 0|0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 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 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 1 0 0 0 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 1 1 1 0 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 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 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1|0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 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 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 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1|0 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 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 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 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1|0 0 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 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 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 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 0 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 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 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1|0 1 0 0 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 1 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 1 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 1 1 1 0 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0|0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 1 1 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 1 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 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0|0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 1 1 1 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 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 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0|0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 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 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1 1 0 1 1 1|0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0|0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 0 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 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 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1|0 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 0 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 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 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0|0 0 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 1 1 1 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 1 0 0|0 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1|0 1 0 1 1 0 1 1 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 1 1 1 0 1 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 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 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 1|0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 1 1|0 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0|0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1 0 1 0 0 0 0 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 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 1 1|0 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 0 0 1 0 0 1 0 0 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 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1|0 1 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 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 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 1 0 0 0 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0|0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 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 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 1 0 0 0 1 1 1 1 1 0 0 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0|0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 0 0 1 0 0 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 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1|0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0|0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 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 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 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1|0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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.
This page is maintained by
Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014