Bounds on the minimum distance of additive quantum codes
Bounds on [[84,52]]2
lower bound: | 7 |
upper bound: | 10 |
Construction
Construction of a [[84,52,7]] quantum code:
[1]: [[85, 53, 8]] quantum code over GF(2^2)
cyclic code of length 85 with generating polynomial x^84 + w^2*x^83 + w^2*x^82 + w^2*x^81 + x^80 + w*x^79 + w*x^78 + x^77 + x^74 + w^2*x^73 + x^72 + x^71 + w^2*x^70 + x^69 + w*x^68 + x^67 + w*x^65 + x^63 + w*x^62 + w*x^61 + w^2*x^60 + x^59 + w^2*x^57 + w^2*x^56 + w^2*x^55 + w^2*x^54 + x^51 + x^50 + w^2*x^49 + x^47 + w*x^46 + x^45 + w^2*x^44 + w*x^43 + w^2*x^42 + w*x^41 + x^40 + x^39 + w^2*x^38 + x^37 + x^35 + w*x^33 + x^32 + w^2*x^31 + x^30 + w^2*x^29 + x^28 + w*x^27 + w^2*x^26 + w^2*x^24 + x^23 + w^2*x^22 + w^2*x^21 + w*x^18 + x^16 + 1
[2]: [[85, 52, 8]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[84, 52, 7]] quantum code over GF(2^2)
Puncturing of [2] at { 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 1 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1|1 1 1 0 1 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 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 1 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 0|0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 1|1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 1 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 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1|1 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 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 1 0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 1|1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 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 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0|0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 1 0 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 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1|1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 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 1 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 0|1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 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 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0|0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 0 0 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 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0|0 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 1 0 1 1 0 1 1 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 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 1 1 0|0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 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 1 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 0 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0|0 1 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 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 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0|0 1 0 1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 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 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1|0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 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 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0|0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 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 1 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1|1 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 0 1 0 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 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0|0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 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 1 0 0 0 0 0 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 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0|0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0 1|1 1 0 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 1 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 1 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 0 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1|0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1]
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[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 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 0|1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 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 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0|1 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 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 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 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 0 1 0 0 1 0 1 1 1 0 0 0 1 1 0 1|1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0]
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[0 0 0 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 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0|1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 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 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0|1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 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 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1|1 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 1 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 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1|0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 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 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0|0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 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 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 0 0|1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 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 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1|1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1 1 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.
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Markus Grassl
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Last change: 23.10.2014