Bounds on the minimum distance of additive quantum codes

Bounds on [[93,65]]2

lower bound:6
upper bound:8

Construction

Construction of a [[93,65,6]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[88, 65, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 19, 20, 26, 27, 29, 33, 35, 37, 40, 43, 48, 50, 51, 54, 55, 56, 58, 59, 60, 61, 66, 68, 73, 74, 77, 79, 80, 89, 90, 91, 100, 102, 113, 118, 120, 121, 122, 123, 128 }
[3]:  [[93, 65, 6]] quantum code over GF(2^2)
     ExtendCode [2] by 5

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0|0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0]
      [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 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 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0]
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      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0|0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 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 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0|0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 0 1 1 1 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 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0|0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0|0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 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 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0|0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 1 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 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0|0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0|0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0]
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last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014