Bounds on the minimum distance of additive quantum codes

Bounds on [[28,15]]2

lower bound:4
upper bound:5

Construction

Construction of a [[28,15,4]] quantum code:
[1]:  [[40, 30, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 40 stacked to height 2 with 16 generating polynomials
[2]:  [[25, 15, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 4, 5, 7, 8, 9, 12, 13, 14, 16, 19, 24, 31, 32 }
[3]:  [[28, 15, 4]] Quantum code over GF(2^2)
     ExtendCode [2] by 3

    stabilizer matrix:

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

last modified: 2005-06-24

Notes


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