Bounds on the minimum distance of additive quantum codes

Bounds on [[60,36]]2

lower bound:6
upper bound:8

Construction

Construction of a [[60,36,6]] quantum code:
[1]:  [[128, 105, 6]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[60, 37, 6]] Quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 4, 5, 7, 8, 9, 10, 14, 18, 19, 23, 24, 25, 26, 27, 31, 33, 34, 35, 36, 40, 42, 43, 45, 47, 49, 50, 52, 53, 54, 55, 57, 59, 62, 64, 65, 66, 67, 68, 69, 71, 75, 78, 80, 81, 84, 85, 87, 88, 89, 90, 93, 95, 96, 100, 101, 102, 105, 108, 110, 115, 116, 118, 121, 124, 126, 128 }
[3]:  [[60, 36, 6]] Quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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