Bounds on the minimum distance of additive quantum codes
Bounds on [[116,27]]2
lower bound: | 16 |
upper bound: | 30 |
Construction
Construction of a [[116,27,16]] quantum code:
[1]: [[113, 29, 16]] quantum code over GF(2^2)
cyclic code of length 113 with generating polynomial x^42 + w*x^41 + w*x^40 + x^38 + w*x^35 + x^33 + x^32 + x^31 + x^30 + w^2*x^29 + w^2*x^28 + x^27 + x^26 + x^25 + w*x^24 + w*x^23 + x^22 + x^21 + x^20 + w*x^19 + w*x^18 + x^17 + x^16 + x^15 + w^2*x^14 + w^2*x^13 + x^12 + x^11 + x^10 + x^9 + w*x^7 + x^4 + w*x^2 + w*x + 1
[2]: [[113, 27, 16]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[116, 27, 16]] 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0|0 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 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