Bounds on the minimum distance of additive quantum codes

Bounds on [[58,45]]2

lower bound:4
upper bound:4

Construction

Construction of a [[58,45,4]] quantum code:
[1]:  [[70, 58, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 70 stacked to height 2 with 4 generating polynomials
[2]:  [[58, 46, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 13, 30, 33, 35, 48, 52, 53, 57, 58, 62, 67, 68 }
[3]:  [[58, 45, 4]] Quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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