Bounds on the minimum distance of additive quantum codes

Bounds on [[61,35]]2

lower bound:6
upper bound:9

Construction

Construction of a [[61,35,6]] quantum code:
[1]:  [[128, 105, 6]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[58, 35, 6]] Quantum code over GF(2^2)
     Shortening of [1] at { 3, 4, 5, 6, 11, 12, 16, 17, 18, 19, 20, 23, 28, 31, 32, 35, 36, 39, 40, 41, 44, 46, 47, 48, 49, 50, 52, 54, 55, 58, 59, 60, 62, 64, 66, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 81, 83, 85, 87, 88, 90, 91, 96, 100, 101, 104, 105, 106, 111, 113, 114, 115, 117, 118, 120, 122, 123, 124, 127, 128 }
[3]:  [[61, 35, 6]] Quantum code over GF(2^2)
     ExtendCode [2] by 3

    stabilizer matrix:

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