Bounds on the minimum distance of additive quantum codes

Bounds on [[43,10]]2

lower bound:8
upper bound:12

Construction

Construction of a [[43,10,8]] quantum code:
[1]:  [[42, 11, 8]] Quantum code over GF(2^2)
     cyclic code of length 42 with generating polynomial w^2*x^40 + x^39 + w^2*x^37 + w^2*x^34 + x^33 + w*x^32 + w*x^29 + w^2*x^26 + x^25 + x^24 + w*x^23 + w*x^22 + w^2*x^21 + w*x^20 + w*x^19 + w^2*x^18 + x^17 + w*x^16 + w*x^15 + 1
[2]:  [[42, 10, 8]] Quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[43, 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 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0|0 0 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 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 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 0|0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 1 1 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 1 1 1 1 0 0 0 0 0 0 1 0 0|0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 1 0 0 1 1 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 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0|0 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 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 0 1 1 0 1 1 1 0 0 0 0 1 1 0|0 0 1 1 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 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 0 0 0 1 1 0 1 1 0 1 0 1 1 0 0 0|0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 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 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 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0|0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 0 0 1 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 1 1 1 0 0 0 1 0 1 0 1 1 0|0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0|0 0 1 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 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 1 0 0 0 0|0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0|0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 0 1 0 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 1 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 1 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 0 1 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 1 0 0 1 1 0 1 1 0 0 0 0|0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 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 1 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 0 0 0|0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 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 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0|0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0|0 0 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0|0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0|0 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 1 0 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 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0|0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0|0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 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 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 0|0 0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 0 0 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0|0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 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 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0|0 0 1 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 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 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0|0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 0 0 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 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0|0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0|0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 0 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 1 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0|0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 0 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 1 0 0 0 1 0 0 1 1 1 1 1 0 1 0|0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 1 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 1 1 0 1 0 0 1 1 1 0 0 1 1 0|0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 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 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|1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 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 0 0 0 0 0|0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0]

last modified: 2006-04-03

Notes


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