Bounds on the minimum distance of additive quantum codes
Bounds on [[115,11]]2
lower bound: | 20 |
upper bound: | 35 |
Construction
Construction of a [[115,11,20]] quantum code:
[1]: [[105, 15, 20]] quantum code over GF(2^2)
constacyclic code generated by x^104 + w^2*x^103 + x^102 + x^100 + w*x^97 + w^2*x^96 + x^94 + x^93 + x^90 + w*x^89 + w*x^88 + w*x^87 + x^86 + x^84 + w*x^82 + x^80 + w^2*x^79 + x^78 + x^76 + x^73 + w*x^69 + w*x^64 + x^62 + w^2*x^61 + w^2*x^60 + x^42 with shift constant w
[2]: [[105, 14, 20]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[115, 14, 20]] quantum code over GF(2^2)
ExtendCode [2] by 10
[4]: [[115, 11, 20]] 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0|0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 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.
This page is maintained by
Markus Grassl
(codes@codetables.de).
Last change: 23.10.2014