Bounds on the minimum distance of additive quantum codes
Bounds on [[99,32]]2
lower bound: | 13 |
upper bound: | 23 |
Construction
Construction of a [[99,32,13]] quantum code:
[1]: [[93, 33, 13]] quantum code over GF(2^2)
cyclic code of length 93 with generating polynomial w^2*x^92 + w^2*x^90 + w^2*x^89 + w^2*x^86 + w^2*x^84 + w^2*x^82 + x^80 + x^79 + w^2*x^78 + w*x^77 + w*x^75 + x^74 + w*x^73 + x^72 + x^71 + w*x^70 + w*x^69 + w^2*x^68 + x^67 + w*x^65 + w*x^64 + w^2*x^63 + w^2*x^62 + x^61 + w^2*x^59 + x^58 + w*x^57 + x^56 + x^55 + x^52 + w^2*x^51 + x^50 + w^2*x^49 + w^2*x^48 + x^47 + x^45 + w^2*x^44 + w^2*x^43 + w^2*x^41 + w^2*x^40 + w^2*x^39 + w^2*x^38 + w*x^37 + w^2*x^36 + w*x^34 + w*x^33 + w^2*x^32 + w*x^31 + x^30 + 1
[2]: [[93, 32, 13]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[99, 32, 13]] quantum code over GF(2^2)
ExtendCode [2] by 6
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 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0|1 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0]
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last modified: 2008-03-09
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