Bounds on the minimum distance of additive quantum codes
Bounds on [[106,29]]2
lower bound: | 14 |
upper bound: | 26 |
Construction
Construction of a [[106,29,14]] quantum code:
[1]: [[105, 33, 14]] quantum code over GF(2^2)
constacyclic code generated by w^2*x^104 + x^103 + x^101 + x^100 + w*x^99 + w*x^96 + w*x^95 + w*x^94 + w*x^93 + w*x^92 + w^2*x^88 + w*x^86 + w^2*x^85 + x^84 + w^2*x^83 + x^82 + w^2*x^81 + x^80 + w*x^79 + w*x^77 + w*x^76 + w*x^75 + x^74 + x^73 + x^72 + w*x^71 + w^2*x^69 + x^15 with shift constant w
[2]: [[105, 32, 14]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[106, 32, 14]] quantum code over GF(2^2)
ExtendCode [2] by 1
[4]: [[106, 29, 14]] quantum code over GF(2^2)
Subcode of [3]
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 1 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0|0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 1 1 1 1 1 0 0]
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last modified: 2022-08-02
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.
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Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014