Bounds on the minimum distance of additive quantum codes

Bounds on [[60,0]]2

lower bound:16
upper bound:22

Construction

Construction of a [[60,0,16]] quantum code:
[1]:  [[60, 0, 16]] self-dual Quantum code over GF(2^2)
     cyclic code of length 60 with generating polynomial w*x^59 + w^2*x^58 + x^57 + x^55 + w^2*x^53 + w^2*x^52 + w*x^51 + w^2*x^50 + w^2*x^49 + w*x^48 + x^46 + w*x^44 + w^2*x^42 + x^41 + w^2*x^40 + w^2*x^39 + x^36 + w^2*x^34 + x^33 + w^2*x^32 + w*x^30 + 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 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 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 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 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 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 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
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      [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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 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 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 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0]
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      [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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0]
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last modified: 2006-04-18

Notes


This page is maintained by Markus Grassl (grassl@ira.uka.de). Last change: 23.10.2014