Bounds on the minimum distance of additive quantum codes
Bounds on [[104,1]]2
| lower bound: | 23 |
| upper bound: | 35 |
Construction
Construction of a [[104,1,23]] quantum code:
[1]: [[98, 0, 24]] self-dual quantum code over GF(2^2)
QuasiCyclicCode of length 98 stacked to height 2 with generating polynomials: x^3 + x + 1, w*x^44 + x^43 + w^2*x^42 + w^2*x^41 + w^2*x^40 + x^39 + w*x^37 + w*x^36 + w^2*x^35 + w^2*x^34 + w^2*x^32 + w^2*x^31 + x^30 + w^2*x^28 + w^2*x^27 + x^25 + w^2*x^22 + w^2*x^21 + x^19 + x^18 + w^2*x^17 + w^2*x^16 + w^2*x^13 + w*x^12 + x^11 + x^10 + w^2*x^9 + w*x^7 + x^5 + w*x^4 + w*x^3 + x^2 + w^2*x, 0, x^46 + x^45 + x^44 + x^42 + x^39 + x^38 + x^37 + x^35 + x^32 + x^31 + x^30 + x^28 + x^25 + x^24 + x^23 + x^21 + x^18 + x^17 + x^16 + x^14 + x^11 + x^10 + x^9 + x^7 + x^4 + x^3 + x^2 + 1
[2]: [[97, 1, 23]] quantum code over GF(2^2)
Shortening of the stabilizer code of [1] at { 98 }
[3]: [[104, 1, 23]] 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 1 1 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 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 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
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last modified: 2024-06-10
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 necessarily 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: 10.06.2024