Bounds on the minimum distance of additive quantum codes
Bounds on [[103,1]]2
lower bound: | 21 |
upper bound: | 35 |
Construction
Construction of a [[103,1,21]] quantum code:
[1]: [[101, 1, 21]] quantum code over GF(2^2)
cyclic code of length 101 with generating polynomials [
w^2*x^100 + w^2*x^99 + x^98 + w*x^96 + x^95 + x^94 + w^2*x^93 + w^2*x^92 + w^2*x^91 + w^2*x^89 + w^2*x^87 + w^2*x^85 + w^2*x^84 + w*x^82 + x^81 + x^79 + w*x^78 + x^77 + x^76 + x^75 + x^74 + w*x^73 + x^72 + x^70 + w*x^69 + w^2*x^67 + w^2*x^66 + w^2*x^64 + w^2*x^62 + w^2*x^60 + w^2*x^59 + w^2*x^58 + x^57 + x^56 + w*x^55 + x^53 + w^2*x^52 + w^2*x^51 + x^50 + 1,
x^100 + x^99 + w*x^98 + w^2*x^96 + w*x^95 + w*x^94 + x^93 + x^92 + x^91 + x^89 + x^87 + x^85 + x^84 + w^2*x^82 + w*x^81 + w*x^79 + w^2*x^78 + w*x^77 + w*x^76 + w*x^75 + w*x^74 + w^2*x^73 + w*x^72 + w*x^70 + w^2*x^69 + x^67 + x^66 + x^64 + x^62 + x^60 + x^59 + x^58 + w*x^57 + w*x^56 + w^2*x^55 + w*x^53 + x^52 + x^51 + w*x^50 + w
]
[2]: [[103, 1, 21]] quantum code over GF(2^2)
ExtendCode [1] by 2
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 0 0 0 0 0 0 0 0 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 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0]
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last modified: 2006-04-07
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