Bounds on the minimum distance of additive quantum codes
Bounds on [[84,32]]2
lower bound: | 11 |
upper bound: | 18 |
Construction
Construction of a [[84,32,11]] quantum code:
[1]: [[85, 33, 12]] quantum code over GF(2^2)
cyclic code of length 85 with generating polynomial x^84 + w^2*x^83 + w*x^82 + w^2*x^80 + w*x^79 + x^76 + x^75 + x^74 + x^73 + x^71 + w^2*x^70 + w*x^68 + w*x^66 + x^64 + w^2*x^63 + w^2*x^62 + x^60 + w^2*x^59 + w^2*x^58 + x^55 + x^54 + w*x^53 + x^52 + w^2*x^49 + x^48 + w*x^47 + w^2*x^44 + w^2*x^43 + x^42 + w^2*x^40 + w^2*x^39 + w*x^37 + w*x^36 + w^2*x^34 + x^32 + x^31 + w*x^30 + w*x^29 + w^2*x^28 + x^27 + x^26 + 1
[2]: [[85, 32, 12]] quantum code over GF(2^2)
Subcode of [1]
[3]: [[84, 32, 11]] quantum code over GF(2^2)
Puncturing of [2] at { 85 }
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 1 0 1 1 1 1 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 1 1|0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 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 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1|0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1]
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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 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 0 0 1 1|1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0]
last modified: 2006-04-03
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