Bounds on the minimum distance of additive quantum codes

Bounds on [[53,30]]2

lower bound:5
upper bound:8

Construction

Construction of a [[53,30,5]] 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]:  [[50, 30, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 4, 5, 6, 7, 11, 12, 14, 15, 16, 17, 20, 22, 27, 29, 33, 40, 41, 42, 44, 45, 48, 52, 53, 54, 61, 62, 64, 66, 67, 68, 69, 71, 73, 74, 76, 77, 82, 83, 84, 87, 92, 93 }
[3]:  [[53, 30, 5]] Quantum code over GF(2^2)
     ExtendCode [2] by 3

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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