Bounds on the minimum distance of additive quantum codes

Bounds on [[111,23]]2

lower bound:16
upper bound:30

Construction

Construction of a [[111,23,16]] quantum code:
[1]:  [[105, 27, 16]] quantum code over GF(2^2)
     constacyclic code generated by w^2*x^104 + w^2*x^103 + w*x^102 + x^101 + x^100 + x^99 + x^98 + x^97 + w*x^96 + x^94 + w^2*x^93 + w*x^91 + w*x^90 + w^2*x^89 + w^2*x^88 + w*x^86 + w^2*x^83 + x^82 + x^81 + w*x^74 + x^73 + x^72 + x^71 + x^70 + w^2*x^68 + x^67 + w^2*x^66 + x^8 with shift constant w
[2]:  [[111, 27, 16]] quantum code over GF(2^2)
     ExtendCode [1] by 6
[3]:  [[111, 23, 16]] quantum code over GF(2^2)
     Subcode of [2]

    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 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0|0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0]
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last modified: 2022-08-02

Notes


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