Bounds on the minimum distance of additive quantum codes
Bounds on [[88,46]]2
lower bound: | 9 |
upper bound: | 14 |
Construction
Construction of a [[88,46,9]] quantum code:
[1]: [[89, 45, 10]] quantum code over GF(2^2)
cyclic code of length 89 with generating polynomial x^87 + w*x^86 + x^85 + x^84 + x^83 + w*x^82 + x^80 + w*x^76 + x^75 + w*x^74 + x^73 + x^71 + x^70 + w^2*x^69 + w^2*x^68 + x^67 + w*x^65 + w*x^64 + x^63 + w*x^61 + x^60 + w^2*x^59 + w^2*x^58 + w*x^57 + w^2*x^56 + w^2*x^54 + w*x^49 + w*x^47 + x^45 + x^44 + x^43 + x^42 + x^41 + x^38 + x^37 + w^2*x^36 + x^35 + w*x^34 + w*x^32 + w^2*x^31 + w*x^30 + w^2*x^29 + x^28 + w*x^27 + w*x^24 + w*x^23 + x^22 + x^21 + w^2*x^20 + w*x^19 + w*x^17 + w*x^16 + x^15 + w*x^14 + x^13 + w^2*x^12 + x^11 + w*x^9 + w*x^8 + w^2*x^7 + w*x^6 + w^2*x^5 + w*x^3 + w*x^2 + w^2*x + w
[2]: [[88, 46, 9]] quantum code over GF(2^2)
Shortening of the stabilizer code of [1] at { 89 }
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 1 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0|1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 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 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1|0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 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 1 1 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0|1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1]
last modified: 2020-10-24
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