Bounds on the minimum distance of additive quantum codes
Bounds on [[91,20]]2
lower bound: | 15 |
upper bound: | 25 |
Construction
Construction of a [[91,20,15]] quantum code:
[1]: [[85, 21, 15]] quantum code over GF(2^2)
cyclic code of length 85 with generating polynomial x^82 + x^81 + x^80 + w^2*x^79 + x^78 + w*x^77 + w^2*x^76 + x^74 + w*x^73 + w*x^72 + w^2*x^71 + w^2*x^69 + w^2*x^68 + x^67 + w*x^66 + w*x^65 + w*x^64 + w*x^63 + x^61 + x^60 + w*x^59 + x^58 + w^2*x^56 + x^55 + w*x^54 + w^2*x^52 + w^2*x^48 + w^2*x^47 + w*x^46 + w*x^45 + w*x^44 + w^2*x^43 + w^2*x^42 + w*x^41 + x^40 + w^2*x^39 + x^38 + w*x^37 + x^36 + x^35 + w*x^34 + w*x^33 + x^32 + 1
[2]: [[85, 20, 15]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[91, 20, 15]] 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 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0|1 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 0 0 0 0 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