Bounds on the minimum distance of additive quantum codes

Bounds on [[45,14]]2

lower bound:8
upper bound:12

Construction

Construction of a [[45,14,8]] quantum code:
[1]:  [[43, 14, 8]] Quantum code over GF(2^2)
     cyclic code of length 43 with generating polynomial x^42 + x^41 + w*x^40 + w*x^38 + w*x^37 + w^2*x^36 + x^35 + w*x^32 + w^2*x^31 + w*x^30 + x^29 + w*x^28 + w^2*x^27 + w*x^26 + x^23 + w^2*x^22 + w*x^21 + w*x^20 + w*x^18 + x^17 + x^16 + x^15 + 1
[2]:  [[45, 14, 8]] Quantum code over GF(2^2)
     ExtendCode [1] by 2

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

last modified: 2006-04-03

Notes


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