Bounds on the minimum distance of additive quantum codes

Bounds on [[101,71]]2

lower bound:6
upper bound:9

Construction

Construction of a [[101,71,6]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[94, 71, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 58, 60, 61, 68, 69, 70, 71, 73, 78, 83, 85, 87, 88, 90, 92, 95, 97, 98, 99, 102, 105, 106, 108, 109, 111, 112, 116, 118, 119, 120, 124, 126, 128 }
[3]:  [[100, 71, 6]] quantum code over GF(2^2)
     ExtendCode [2] by 6
[4]:  [[101, 71, 6]] quantum code over GF(2^2)
     ExtendCode [3] by 1

    stabilizer matrix:

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