Bounds on the minimum distance of additive quantum codes
Bounds on [[96,2]]2
lower bound: | 21 |
upper bound: | 32 |
Construction
Construction of a [[96,2,21]] quantum code:
[1]: [[93, 3, 21]] quantum code over GF(2^2)
cyclic code of length 93 with generating polynomial x^45 + w*x^44 + w^2*x^41 + w^2*x^39 + x^38 + x^37 + w^2*x^36 + x^35 + w*x^34 + w^2*x^32 + w^2*x^31 + w^2*x^30 + x^29 + x^27 + w^2*x^25 + w*x^24 + w^2*x^23 + x^22 + x^20 + w^2*x^18 + x^17 + w^2*x^14 + w*x^12 + w^2*x^11 + w^2*x^10 + w^2*x^9 + w*x^8 + w*x^4 + w*x^2 + w^2*x + 1
[2]: [[93, 2, 21]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[96, 2, 21]] quantum code over GF(2^2)
ExtendCode [2] by 3
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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 1 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 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 0 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 1 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0]
last modified: 2013-12-09
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