Bounds on the minimum distance of additive quantum codes

Bounds on [[98,84]]2

lower bound:4
upper bound:4

Construction

Construction of a [[98,84,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[96, 84, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 4, 10, 12, 14, 32, 36, 80, 83, 94, 97, 98, 100, 101, 102, 103, 105, 108, 109, 112, 113, 114, 115, 116, 117, 120, 122, 123, 124, 125, 126 }
[3]:  [[98, 84, 4]] quantum code over GF(2^2)
     ExtendCode [2] by 2

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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