Bounds on the minimum distance of additive quantum codes

Bounds on [[60,38]]2

lower bound:5
upper bound:8

Construction

Construction of a [[60,38,5]] 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]:  [[58, 38, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 5, 6, 10, 12, 16, 20, 25, 26, 27, 29, 31, 34, 36, 42, 44, 46, 47, 51, 54, 56, 59, 61, 63, 68, 69, 70, 72, 74, 75, 79, 80, 84, 86, 90 }
[3]:  [[60, 38, 5]] Quantum code over GF(2^2)
     ExtendCode [2] by 2

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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