Bounds on the minimum distance of additive quantum codes

Bounds on [[101,4]]2

lower bound:20
upper bound:34

Construction

Construction of a [[101,4,20]] quantum code:
[1]:  [[93, 3, 21]] quantum code over GF(2^2)
     cyclic code of length 93 with generating polynomial x^45 + w*x^44 + w^2*x^41 + w^2*x^39 + x^38 + x^37 + w^2*x^36 + x^35 + w*x^34 + w^2*x^32 + w^2*x^31 + w^2*x^30 + x^29 + x^27 + w^2*x^25 + w*x^24 + w^2*x^23 + x^22 + x^20 + w^2*x^18 + x^17 + w^2*x^14 + w*x^12 + w^2*x^11 + w^2*x^10 + w^2*x^9 + w*x^8 + w*x^4 + w*x^2 + w^2*x + 1
[2]:  [[92, 4, 20]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 93 }
[3]:  [[101, 4, 20]] quantum code over GF(2^2)
     ExtendCode [2] by 9

    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 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 0 0 1 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 0 0 1 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0]
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last modified: 2015-05-28

Notes


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