Bounds on the minimum distance of additive quantum codes
Bounds on [[92,15]]2
lower bound: | 16 |
upper bound: | 27 |
Construction
Construction of a [[92,15,16]] quantum code:
[1]: [[85, 17, 16]] quantum code over GF(2^2)
cyclic code of length 85 with generating polynomials [
x^84 + w^2*x^83 + x^82 + w^2*x^80 + w^2*x^79 + x^78 + w^2*x^77 + x^75 + x^73 + w^2*x^72 + w*x^70 + w^2*x^69 + w*x^67 + w*x^66 + w^2*x^65 + w*x^64 + x^61 + w^2*x^60 + w^2*x^59 + w^2*x^58 + x^57 + w^2*x^56 + x^55 + x^54 + w*x^53 + w^2*x^51 + w*x^50 + w^2*x^49 + w^2*x^48 + w^2*x^45 + x^44 + w*x^43 + w*x^42 + w*x^41 + w*x^39 + w*x^37 + w^2*x^36 + w*x^35 + x^34 + 1,
w*x^84 + x^83 + w*x^82 + x^80 + x^79 + w*x^78 + x^77 + w*x^75 + w*x^73 + x^72 + w^2*x^70 + x^69 + w^2*x^67 + w^2*x^66 + x^65 + w^2*x^64 + w*x^61 + x^60 + x^59 + x^58 + w*x^57 + x^56 + w*x^55 + w*x^54 + w^2*x^53 + x^51 + w^2*x^50 + x^49 + x^48 + x^45 + w*x^44 + w^2*x^43 + w^2*x^42 + w^2*x^41 + w^2*x^39 + w^2*x^37 + x^36 + w^2*x^35 + w*x^34 + w
]
[2]: [[85, 15, 16]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[92, 15, 16]] quantum code over GF(2^2)
ExtendCode [2] by 7
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 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 0 1 0 1 1 1 0 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 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 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