Bounds on the minimum distance of additive quantum codes

Bounds on [[52,29]]2

lower bound:6
upper bound:8

Construction

Construction of a [[52,29,6]] quantum code:
[1]:  [[128, 105, 6]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[52, 29, 6]] Quantum code over GF(2^2)
     Shortening of [1] at { 2, 4, 5, 6, 8, 11, 14, 15, 17, 18, 20, 22, 26, 27, 28, 31, 32, 33, 36, 38, 40, 43, 45, 46, 49, 50, 51, 53, 57, 58, 59, 63, 66, 67, 68, 69, 71, 74, 76, 77, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 92, 94, 95, 99, 100, 101, 102, 103, 104, 105, 106, 110, 111, 112, 113, 115, 116, 118, 120, 121, 122, 124, 125, 127, 128 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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