Bounds on the minimum distance of additive quantum codes

Bounds on [[89,67]]2

lower bound:5
upper bound:7

Construction

Construction of a [[89,67,5]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[90, 67, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 37, 58, 62, 65, 70, 73, 74, 78, 79, 80, 81, 82, 83, 84, 85, 88, 91, 92, 93, 94, 96, 97, 100, 101, 103, 104, 107, 109, 111, 114, 115, 116, 118, 119, 123, 126, 127, 128 }
[3]:  [[89, 67, 5]] quantum code over GF(2^2)
     Puncturing of [2] at { 90 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014