Bounds on the minimum distance of additive quantum codes

Bounds on [[90,78]]2

lower bound:4
upper bound:4

Construction

Construction of a [[90,78,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[90, 78, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 12, 13, 14, 21, 24, 28, 30, 31, 35, 39, 42, 47, 49, 50, 52, 55, 56, 58, 64, 68, 74, 75, 83, 85, 92, 95, 96, 98, 99, 103, 108, 111, 112, 117, 121, 126 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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