Bounds on the minimum distance of additive quantum codes

Bounds on [[104,34]]2

lower bound:13
upper bound:24

Construction

Construction of a [[104,34,13]] quantum code:
[1]:  [[105, 33, 14]] quantum code over GF(2^2)
     constacyclic code generated by w^2*x^104 + x^103 + x^101 + x^100 + w*x^99 + w*x^96 + w*x^95 + w*x^94 + w*x^93 + w*x^92 + w^2*x^88 + w*x^86 + w^2*x^85 + x^84 + w^2*x^83 + x^82 + w^2*x^81 + x^80 + w*x^79 + w*x^77 + w*x^76 + w*x^75 + x^74 + x^73 + x^72 + w*x^71 + w^2*x^69 + x^15 with shift constant w
[2]:  [[104, 34, 13]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 105 }

    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 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0|0 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 0 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 0 0 0 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 0 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0|1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1]
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last modified: 2022-08-03

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014