Bounds on the minimum distance of additive quantum codes
Bounds on [[71,15]]2
lower bound: | 12 |
upper bound: | 20 |
Construction
Construction of a [[71,15,12]] quantum code:
[1]: [[68, 16, 12]] quantum code over GF(2^2)
QuasiCyclicCode of length 68 with generating polynomials: x^32 + x^29 + x^28 + x^27 + x^7, w*x^33 + w*x^32 + x^31 + x^30 + x^29 + w^2*x^28 + x^27 + w*x^26 + w^2*x^25 + x^24 + x^23 + w*x^19 + x^18 + w^2*x^17 + x^16 + x^15 + w^2*x^14 + x^13 + w^2*x^12 + w^2*x^11 + x^10 + x^9 + x^8 + w^2*x^6 + w^2*x^5 + x + 1
[2]: [[68, 15, 12]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[71, 15, 12]] quantum code over GF(2^2)
ExtendCode [2] by 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 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 0 0|0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0]
last modified: 2014-12-15
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