Bounds on the minimum distance of additive quantum codes

Bounds on [[40,15]]2

lower bound:7
upper bound:9

Construction

Construction of a [[40,15,7]] quantum code:
[1]:  [[39, 15, 7]] Quantum code over GF(2^2)
     constacyclic code generated by w^2*x^37 + x^36 + x^35 + x^34 + x^32 + w*x^31 + w^2*x^30 + w*x^29 + w*x^28 + x^27 + x^26 + w*x^25 + w*x^24 + x^22 + x^21 + w^2*x^20 + w*x^18 + w^2*x^17 + w^2*x^14 + x^13 + w^2*x^12 + 1 with shift constant w
[2]:  [[40, 15, 7]] Quantum code over GF(2^2)
     ExtendCode [1] 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 1 1 1 1 1 0 0 1 1 0 0 0 1 0 1 0|1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 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 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0|1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 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 1 1 1 1 1 0 0 1 1 0 0 0 1 0|0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 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 1 1 1 0 0 1 1 0 1 0 1 1 1 0 1 0|1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 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 1 1 0 0 1 1 0 1 0 1 1 1 0 0|1 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 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 1 1 0 0 1 1 0 1 0 1 1 1 0|0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 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 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0|1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 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 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0|0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 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 1 1 1 0 0 1 0 1 0 1 0 1 1 0|1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 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 1 1 1 0 0 1 0 1 0 1 0 1 0|1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 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 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0|1 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 0 1 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 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0|1 1 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 0 1 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 1 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0|1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 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 1 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0|0 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 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 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 1 0|0 0 1 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 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 0 0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 1 0|1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 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 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0|1 1 1 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 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 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 0 1 1 0|0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 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 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0|1 0 0 1 0 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 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 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 0|0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 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 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 1 0 0|1 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 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 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 1 0|0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 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 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0|1 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 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 1 1 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0|0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 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 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]

last modified: 2006-04-03

Notes


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