Bounds on the minimum distance of additive quantum codes

Bounds on [[63,8]]2

lower bound:13
upper bound:20

Construction

Construction of a [[63,8,13]] quantum code:
[1]:  [[63, 8, 13]] Quantum code over GF(2^2)
     cyclic code of length 63 with generating polynomial x^62 + w*x^61 + w*x^59 + w*x^58 + x^57 + w*x^55 + x^54 + x^53 + w*x^52 + w*x^51 + w^2*x^50 + x^48 + x^46 + x^44 + w^2*x^43 + w^2*x^42 + x^41 + w^2*x^40 + x^39 + w^2*x^37 + x^36 + w*x^35 + x^33 + w^2*x^31 + w*x^29 + w*x^27 + w

    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 1 0 0 1 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 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 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 1 1 0 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
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      [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 1 1 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0]
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      [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 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1]
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      [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 0 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 0 1 0 1|0 1 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1]
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last modified: 2008-02-16

Notes


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