Bounds on the minimum distance of additive quantum codes

Bounds on [[56,41]]2

lower bound:4
upper bound:5

Construction

Construction of a [[56,41,4]] quantum code:
[1]:  [[62, 50, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 62 stacked to height 2 with 4 generating polynomials
[2]:  [[54, 42, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 14, 27, 30, 31, 55, 57, 58, 62 }
[3]:  [[54, 41, 4]] Quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[56, 41, 4]] Quantum code over GF(2^2)
     ExtendCode [3] by 2

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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