Bounds on the minimum distance of additive quantum codes
Bounds on [[190,124]]2
| lower bound: | 10 |
| upper bound: | 20 |
Construction
Construction of a [[190,124,10]] quantum code:
[1]: [[183, 123, 11]] quantum code over GF(2^2)
constacyclic code generated by x^30 + w*x^29 + x^28 + w*x^27 + x^25 + w^2*x^24 + w*x^22 + w^2*x^21 + w^2*x^20 + w^2*x^19 + w^2*x^16 + w*x^15 + x^14 + w^2*x^13 + w*x^12 + w^2*x^10 + x^8 + w*x^7 + w*x^6 + w*x^5 + w*x^4 + w^2*x^3 + w*x^2 + w*x + w with shift constant w
[2]: [[182, 124, 10]] quantum code over GF(2^2)
Shortening of the stabilizer code of [1] at { 183 }
[3]: [[190, 124, 10]] quantum code over GF(2^2)
ExtendCode [2] by 8
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 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0]
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last modified: 2024-05-08
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