Bounds on the minimum distance of additive quantum codes

Bounds on [[37,10]]2

lower bound:8
upper bound:10

Construction

Construction of a [[37,10,8]] quantum code:
[1]:  [[36, 12, 8]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[36, 10, 8]] Quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[37, 10, 8]] Quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-07

Notes


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