Bounds on the minimum distance of additive quantum codes

Bounds on [[51,35]]2

lower bound:4
upper bound:6

Construction

Construction of a [[51,35,4]] quantum code:
[1]:  [[85, 69, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 85 with 4 generating polynomials
[2]:  [[51, 35, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 4, 5, 7, 12, 14, 15, 18, 22, 26, 28, 29, 30, 31, 32, 33, 36, 39, 40, 41, 44, 54, 58, 59, 61, 63, 64, 68, 70, 73, 78, 81, 83, 85 }

    stabilizer matrix:

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