Bounds on the minimum distance of additive quantum codes

Bounds on [[100,32]]2

lower bound:13
upper bound:23

Construction

Construction of a [[100,32,13]] quantum code:
[1]:  [[93, 33, 13]] quantum code over GF(2^2)
     cyclic code of length 93 with generating polynomial w^2*x^92 + w^2*x^90 + w^2*x^89 + w^2*x^86 + w^2*x^84 + w^2*x^82 + x^80 + x^79 + w^2*x^78 + w*x^77 + w*x^75 + x^74 + w*x^73 + x^72 + x^71 + w*x^70 + w*x^69 + w^2*x^68 + x^67 + w*x^65 + w*x^64 + w^2*x^63 + w^2*x^62 + x^61 + w^2*x^59 + x^58 + w*x^57 + x^56 + x^55 + x^52 + w^2*x^51 + x^50 + w^2*x^49 + w^2*x^48 + x^47 + x^45 + w^2*x^44 + w^2*x^43 + w^2*x^41 + w^2*x^40 + w^2*x^39 + w^2*x^38 + w*x^37 + w^2*x^36 + w*x^34 + w*x^33 + w^2*x^32 + w*x^31 + x^30 + 1
[2]:  [[93, 32, 13]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[100, 32, 13]] quantum code over GF(2^2)
     ExtendCode [2] by 7

    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 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0|1 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0|0 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0|1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0]
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last modified: 2008-03-09

Notes


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