Bounds on the minimum distance of additive quantum codes
Bounds on [[93,50]]2
lower bound: | 9 |
upper bound: | 14 |
Construction
Construction of a [[93,50,9]] quantum code:
[1]: [[93, 51, 9]] quantum code over GF(2^2)
cyclic code of length 93 with generating polynomial x^92 + w^2*x^90 + w^2*x^88 + x^85 + x^84 + w^2*x^83 + w*x^82 + w^2*x^81 + w^2*x^80 + w^2*x^79 + w^2*x^77 + x^75 + w*x^73 + x^72 + w^2*x^71 + x^70 + w*x^69 + w*x^67 + w*x^66 + w*x^65 + w*x^64 + w*x^63 + w*x^62 + w^2*x^61 + w*x^58 + w*x^57 + x^56 + w*x^54 + w^2*x^53 + x^52 + w*x^49 + x^46 + w^2*x^45 + x^44 + x^43 + w*x^39 + w^2*x^38 + w*x^37 + w^2*x^36 + w*x^35 + x^34 + w*x^32 + w^2*x^30 + w^2*x^29 + x^28 + x^26 + x^25 + w^2*x^23 + w*x^22 + 1
[2]: [[93, 50, 9]] 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 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 1 0|1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 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 1 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1|1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 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 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 1 1|1 0 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 0 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 0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1|1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 1 1]
last modified: 2008-02-21
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