Bounds on the minimum distance of additive quantum codes

Bounds on [[37,0]]2

lower bound:11
upper bound:14

Construction

Construction of a [[37,0,11]] quantum code:
[1]:  [[37, 0, 11]] self-dual Quantum code over GF(2^2)
     cyclic code of length 37 with generating polynomial x^35 + w^2*x^34 + w^2*x^33 + x^32 + w*x^31 + w*x^29 + x^26 + w^2*x^25 + w^2*x^22 + w*x^20 + w*x^18 + w*x^17 + 1

    stabilizer matrix:

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

last modified: 2006-04-06

Notes


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