Bounds on the minimum distance of additive quantum codes
Bounds on [[76,26]]2
| lower bound: | 11 |
| upper bound: | 18 |
Construction
Construction of a [[76,26,11]] quantum code:
[1]: [[75, 27, 11]] quantum code over GF(2^2)
QuasiCyclicCode of length 75 stacked to height 3 with generating polynomials: 1, w*x + w^2, w*x^21 + w*x^20 + w^2*x^19 + x^17 + x^16 + w*x^15 + w*x^11 + x^10 + x^9 + x^8 + w^2*x^7 + w*x^6 + x^5 + w^2*x^4 + x^2 + 1, 0, x^2 + w*x + 1, w*x^21 + x^20 + w^2*x^19 + w^2*x^17 + w^2*x^16 + w^2*x^13 + w*x^12 + w^2*x^11 + w*x^10 + w*x^7 + x^6 + x^4 + w^2*x^3 + x^2 + w*x + w, 0, 0, x^22 + w*x^21 + x^20 + x^17 + w*x^16 + x^15 + x^12 + w*x^11 + x^10 + x^7 + w*x^6 + x^5 + x^2 + w*x + 1
[2]: [[75, 26, 11]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[76, 26, 11]] quantum code over GF(2^2)
ExtendCode [2] by 1
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 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1 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 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0]
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[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
last modified: 2024-06-17
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