Bounds on the minimum distance of additive quantum codes
Bounds on [[119,0]]2
lower bound: | 20 |
upper bound: | 41 |
Construction
Construction of a [[119,0,20]] quantum code:
[1]: [[119, 1, 20]] quantum code over GF(2^2)
cyclic code of length 119 with generating polynomial x^59 + w^2*x^58 + x^57 + w*x^54 + w^2*x^53 + w^2*x^52 + w^2*x^49 + w^2*x^48 + x^47 + w*x^46 + x^43 + w^2*x^40 + x^39 + w^2*x^38 + w*x^37 + x^36 + w*x^35 + w^2*x^31 + w^2*x^30 + w*x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + w*x^21 + x^20 + x^19 + x^18 + x^17 + w*x^15 + w*x^14 + w^2*x^13 + w^2*x^12 + w*x^11 + w^2*x^10 + w^2*x^9 + w*x^6 + w*x^5 + x^2 + w^2*x + 1
[2]: [[119, 0, 20]] self-dual quantum code over GF(2^2)
Subcode of [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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 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 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0]
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last modified: 2022-08-01
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