Bounds on the minimum distance of additive quantum codes

Bounds on [[49,23]]2

lower bound:7
upper bound:9

Construction

Construction of a [[49,23,7]] quantum code:
[1]:  [[47, 23, 7]] quantum code over GF(2^2)
     cyclic code of length 47 with generating polynomial x^46 + x^43 + w*x^42 + w*x^40 + x^39 + x^38 + w^2*x^36 + w*x^35 + w^2*x^33 + x^32 + x^31 + x^30 + w*x^29 + x^26 + x^25 + w*x^24 + w^2*x^23 + w^2*x^22 + x^21 + x^19 + x^17 + w*x^16 + w^2*x^15 + w^2*x^13 + x^6
[2]:  [[49, 23, 7]] 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 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0|1 0 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 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 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0|1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 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 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0|0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 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 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 0|1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 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 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 0 0|0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 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 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 0|1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 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 1 0 1 0 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0|1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 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 1 0 1 0 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 0|1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 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 1 0 1 0 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0|0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 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 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 1 0 0 0 0|0 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1 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 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 1 0 0 0|0 0 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1 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 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 1 0 0|0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1 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 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0|1 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 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 1 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0|0 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0|0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 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 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0|1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 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 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0|0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 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 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0|0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 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 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0|1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 0 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 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0|0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 1 0 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 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0|1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 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 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0|0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 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 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0|0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 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 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0|0 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 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 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 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]

last modified: 2022-08-02

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014