Bounds on the minimum distance of additive quantum codes

Bounds on [[104,72]]2

lower bound:6
upper bound:10

Construction

Construction of a [[104,72,6]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[96, 73, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 14, 58, 59, 60, 61, 63, 67, 69, 71, 81, 82, 84, 86, 88, 89, 90, 92, 94, 95, 98, 99, 100, 104, 106, 107, 111, 114, 118, 121, 124, 125, 128 }
[3]:  [[96, 72, 6]] quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[100, 72, 6]] quantum code over GF(2^2)
     ExtendCode [3] by 4
[5]:  [[104, 72, 6]] quantum code over GF(2^2)
     ExtendCode [4] by 4

    stabilizer matrix:

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