Bounds on the minimum distance of additive quantum codes

Bounds on [[55,31]]2

lower bound:6
upper bound:8

Construction

Construction of a [[55,31,6]] quantum code:
[1]:  [[128, 105, 6]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[54, 31, 6]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 3, 5, 6, 7, 8, 9, 10, 11, 12, 17, 21, 24, 26, 27, 28, 29, 30, 32, 35, 38, 44, 45, 46, 48, 49, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 69, 70, 74, 76, 77, 78, 79, 80, 83, 84, 85, 87, 88, 89, 90, 92, 93, 94, 96, 99, 100, 101, 104, 108, 109, 110, 111, 112, 113, 115, 116, 119, 120, 121, 122, 127, 128 }
[3]:  [[55, 31, 6]] Quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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