Bounds on the minimum distance of additive quantum codes

Bounds on [[57,35]]2

lower bound:5
upper bound:8

Construction

Construction of a [[57,35,5]] quantum code:
[1]:  [[87, 59, 6]] Quantum code over GF(2^2)
     quasicyclic code of length 87 with 2 generating polynomials
[2]:  [[84, 62, 5]] Quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 3, 24, 30 }
[3]:  [[57, 35, 5]] Quantum code over GF(2^2)
     Shortening of [2] at { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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