Bounds on the minimum distance of additive quantum codes
Bounds on [[117,53]]2
lower bound: | 12 |
upper bound: | 21 |
Construction
Construction of a [[117,53,12]] quantum code:
[1]: [[113, 57, 12]] quantum code over GF(2^2)
cyclic code of length 113 with generating polynomial w*x^112 + x^111 + w*x^109 + w*x^108 + w*x^105 + w*x^103 + w^2*x^101 + x^99 + w*x^98 + x^96 + x^94 + w^2*x^92 + w*x^89 + w^2*x^88 + w*x^86 + x^85 + w*x^83 + x^82 + w^2*x^81 + w^2*x^80 + x^79 + w*x^78 + w*x^77 + x^74 + w*x^73 + w*x^68 + x^67 + w*x^64 + w*x^63 + x^62 + w^2*x^61 + w^2*x^60 + x^59 + w*x^58 + x^56 + w*x^55 + w^2*x^53 + w*x^52 + w^2*x^49 + x^47 + x^45 + w*x^43 + x^42 + w^2*x^40 + w*x^38 + w*x^36 + w*x^33 + w*x^32 + x^30 + w*x^29 + x^28 + 1
[2]: [[113, 53, 12]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[117, 53, 12]] quantum code over GF(2^2)
ExtendCode [2] by 4
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 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 0 0 0 0|1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0]
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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