Bounds on the minimum distance of additive quantum codes

Bounds on [[101,31]]2

lower bound:13
upper bound:24

Construction

Construction of a [[101,31,13]] quantum code:
[1]:  [[91, 31, 13]] quantum code over GF(2^2)
     cyclic code of length 91 with generating polynomial w*x^90 + w*x^89 + w*x^88 + w^2*x^87 + w^2*x^86 + w*x^85 + x^84 + w^2*x^83 + w^2*x^80 + x^79 + w^2*x^77 + w^2*x^76 + x^75 + x^73 + w*x^72 + x^71 + x^70 + x^69 + x^68 + w^2*x^67 + w^2*x^66 + w^2*x^65 + x^64 + x^63 + w*x^62 + w*x^61 + w^2*x^60 + x^59 + w*x^58 + x^57 + w*x^56 + x^55 + w*x^54 + w^2*x^52 + w*x^50 + x^49 + x^47 + x^45 + w^2*x^44 + w*x^42 + x^41 + x^40 + x^39 + x^38 + w^2*x^37 + x^36 + w*x^35 + x^34 + w*x^33 + w^2*x^32 + x^30 + 1
[2]:  [[101, 31, 13]] quantum code over GF(2^2)
     ExtendCode [1] by 10

    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 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0|1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0|1 0 1 1 0 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0]
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last modified: 2006-04-03

Notes


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