Bounds on the minimum distance of additive quantum codes

Bounds on [[58,33]]2

lower bound:6
upper bound:8

Construction

Construction of a [[58,33,6]] quantum code:
[1]:  [[128, 105, 6]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[56, 33, 6]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 4, 7, 8, 9, 12, 14, 15, 16, 19, 20, 21, 22, 23, 24, 26, 27, 30, 32, 33, 34, 39, 40, 41, 42, 43, 44, 46, 47, 48, 50, 51, 52, 53, 54, 57, 61, 62, 67, 69, 71, 73, 74, 76, 77, 79, 80, 81, 82, 83, 84, 85, 86, 91, 93, 95, 97, 100, 102, 103, 105, 106, 108, 112, 114, 115, 117, 121, 122, 123, 127 }
[3]:  [[58, 33, 6]] 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 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 1 0 0 0|0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 0 0]
      [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0|0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0|0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0|0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 0 0]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0|0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0 0]
      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0|0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0]
      [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0|0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 0 0]
      [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 0 0|0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 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 1 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0|0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0]
      [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0|0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 0 0|0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 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 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 1 1 0 1 1 1 0 0 0 1 1 0 0 1 0 0 0|0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0|0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 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 1 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 0 0|0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 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 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0|0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 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 0 0 0 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 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|1 0 0 0 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 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 1 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 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 0 0 0 0 0 0 0 0|0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 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 1 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 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