Bounds on the minimum distance of additive quantum codes

Bounds on [[56,25]]2

lower bound:8
upper bound:11

Construction

Construction of a [[56,25,8]] quantum code:
[1]:  [[55, 25, 8]] quantum code over GF(2^2)
     cyclic code of length 55 with generating polynomial w*x^53 + w*x^52 + w*x^51 + w^2*x^50 + w*x^49 + w^2*x^48 + x^47 + w^2*x^45 + w^2*x^43 + x^42 + w*x^40 + x^39 + w^2*x^38 + x^36 + x^35 + w*x^34 + w*x^33 + w^2*x^32 + w*x^31 + w^2*x^28 + w^2*x^24 + x^23 + x^22 + w^2*x^21 + w^2*x^20 + x^18 + w*x^16 + w*x^15 + w*x^14 + w
[2]:  [[56, 25, 8]] 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 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 0|0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 0 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 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0|1 1 0 1 0 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 1 0 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 1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0|1 1 1 0 1 0 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 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 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0|1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 0 0 1 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 0 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0|0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 1 0 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 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0|0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 1 0 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 1 0 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 0 1 1 1 0|1 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 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 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0|0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 0 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 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0|1 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 0 0 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 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0|1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 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 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0|0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 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 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0|0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 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 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0|1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 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 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 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0|0 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 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 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 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0|1 0 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 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 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0 0|0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0|0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0|1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 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 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0|1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0|0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 1 1 0|1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 1 1 0 0 0|1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 1 1 0 0|1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 1 1 0|1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 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 1 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0|1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 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 1 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0|1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 0 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 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0|0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 0 0 1 0 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 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 0|1 1 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 1 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 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0|1 0 0 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 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 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0|1 1 0 0 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 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]

last modified: 2022-08-02

Notes


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