Bounds on the minimum distance of additive quantum codes

Bounds on [[56,0]]2

lower bound:15
upper bound:20

Construction

Construction type: Harada

Construction of a [[56,0,15]] quantum code:
[1]:  [[56, 0, 15]] self-dual Quantum code over GF(2^2)
     cyclic code of length 56 with generating polynomial x^55 + x^54 + x^50 + x^49 + x^45 + x^43 + x^42 + x^41 + x^40 + x^37 + x^35 + x^31 + x^29 + x^27 + x^25 + x^21 + x^19 + x^16 + x^15 + x^14 + x^13 + x^11 + x^7 + x^6 + x^2 + x + 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 1 0|0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 1 1 0 1 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 0 0 0 0 0 0 0 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 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0|0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 0 1 0 1 1 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 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 0 1 0 1 1]
      [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 0|0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 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|0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1]
      [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 1 0|0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 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 1|0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1]
      [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 0|0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 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 1|0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 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 1 0|0 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 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 1|0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 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 1 0|0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1]
      [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 1|0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 1 1]
      [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 1 0|0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 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 1|0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 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 1 0|0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1]
      [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 1|0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 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 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 1 0|0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 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 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 1|0 0 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 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 1 0|0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 1 0 1 1 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 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|0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 1 0 1 1 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 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 1 0|0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 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 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 1|0 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 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 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 1 0|0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 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 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 1|0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 1 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 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 1 0|0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0]
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last modified: 2011-06-29

Notes


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