Bounds on the minimum distance of additive quantum codes

Bounds on [[61,34]]2

lower bound:6
upper bound:9

Construction

Construction of a [[61,34,6]] quantum code:
[1]:  [[96, 70, 6]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[60, 34, 6]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 6, 7, 10, 11, 12, 14, 17, 25, 30, 31, 32, 33, 38, 39, 42, 43, 44, 46, 49, 57, 62, 63, 64, 65, 70, 71, 74, 75, 76, 78, 81, 89, 94, 95, 96 }
[3]:  [[61, 34, 6]] Quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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