Bounds on the minimum distance of additive quantum codes

Bounds on [[51,39]]2

lower bound:4
upper bound:4

Construction

Construction of a [[51,39,4]] quantum code:
[1]:  [[63, 51, 4]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[51, 39, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 20, 26, 37, 38, 40, 48, 51, 56, 58, 61, 62 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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