Bounds on the minimum distance of additive quantum codes

Bounds on [[58,37]]2

lower bound:5
upper bound:7

Construction

Construction of a [[58,37,5]] quantum code:
[1]:  [[93, 73, 5]] Quantum code over GF(2^2)
     quasicyclic code of length 93 stacked to height 2 with 6 generating polynomials
[2]:  [[57, 37, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 4, 11, 14, 16, 18, 19, 20, 21, 24, 28, 31, 36, 40, 41, 46, 48, 53, 54, 55, 56, 58, 60, 62, 63, 64, 67, 71, 74, 75, 78, 85, 88, 90, 92, 93 }
[3]:  [[58, 37, 5]] Quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 1 0 0 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 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 0|0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 0]
      [0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 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 1 0 1 1 0 1 0 1 0 1 1 1 0|1 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 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 1 1 1 0 1 1 1 0 1 1 0 0 1 0|0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 0]
      [0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 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 0 1 0 0 0 1 0 0|1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0]
      [0 0 0 0 1 0 0 0 0 0 0 1 1 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 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 0|0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0]
      [0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 1 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 0 0 0 0 0 0 1 1 0 0 0 0 0 0|0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 0 1 0]
      [0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 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 0 0 0 0 0 0 0 1 1 0 1 0|1 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0]
      [0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 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 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 0|1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0]
      [0 0 0 0 0 0 0 0 0 1 0 0 1 0 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 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0|1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0|0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 1 1 0|0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 0 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 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0|0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0|1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 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 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0|1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 1 1 0 0 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 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0|0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 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 1 0 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0|0 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 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 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1 0 1 0|0 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 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 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0|0 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 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 1 0 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0|1 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 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 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0|1 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 0 0 0 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 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0]

last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (grassl@ira.uka.de). Last change: 23.10.2014