Bounds on the minimum distance of additive quantum codes

Bounds on [[51,25]]2

lower bound:7
upper bound:9

Construction

Construction of a [[51,25,7]] quantum code:
[1]:  [[51, 26, 7]] quantum code over GF(2^2)
     cyclic code of length 51 with generating polynomial w^2*x^47 + w*x^43 + w*x^41 + x^40 + x^38 + w^2*x^37 + x^36 + w^2*x^35 + w*x^34 + w^2*x^33 + w*x^32 + w^2*x^30 + x^29 + w^2*x^28 + x^27 + w*x^24 + w*x^23 + w*x^22 + w^2*x^21 + x^20 + w^2*x^19 + x^18 + w^2*x^17 + w^2*x^16 + w*x^15 + w*x^14 + x^13 + w*x^12 + w
[2]:  [[51, 25, 7]] quantum code over GF(2^2)
     Subcode of [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 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1|0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 1 1 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 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 0 0 0|0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 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 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 1 1 1 0|0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 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 0 1 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 0|0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 1 0 0 0 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 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 0 1|0 0 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 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 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 1 0|0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 1 1 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 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 0|0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 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 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 1|0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 0 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 1 0 1 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1|0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 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 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0|0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 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 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0|0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 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 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1|0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1 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 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1|0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 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 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0|0 1 1 1 1 1 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 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 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1|0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 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 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 1 1 1 0|0 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 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 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1|0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 0 1 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 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 0|0 1 1 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 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 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0|0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0 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 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1|0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0 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 1 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1|0 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 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 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1|0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 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 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 0|0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 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 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1|0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 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 0 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 1 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 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 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 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]

last modified: 2022-08-02

Notes


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