Bounds on the minimum distance of additive quantum codes

Bounds on [[51,29]]2

lower bound:5
upper bound:8

Construction

Construction of a [[51,29,5]] 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]:  [[49, 29, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 2, 4, 6, 9, 10, 12, 16, 17, 18, 20, 21, 22, 23, 25, 29, 31, 32, 33, 35, 37, 38, 42, 43, 47, 49, 53, 57, 62, 63, 64, 65, 66, 68, 72, 74, 76, 78, 80, 83, 84, 86, 90, 91, 92 }
[3]:  [[51, 29, 5]] Quantum code over GF(2^2)
     ExtendCode [2] by 2

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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