Bounds on the minimum distance of additive quantum codes

Bounds on [[53,37]]2

lower bound:4
upper bound:6

Construction

Construction of a [[53,37,4]] quantum code:
[1]:  [[85, 69, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 85 with 4 generating polynomials
[2]:  [[53, 37, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 2, 4, 7, 12, 15, 17, 20, 21, 22, 26, 28, 31, 33, 38, 43, 44, 46, 47, 49, 50, 54, 55, 57, 58, 60, 61, 66, 69, 70, 73, 82, 85 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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