Bounds on the minimum distance of additive quantum codes

Bounds on [[57,0]]2

lower bound:15
upper bound:20

Construction

Construction type: Harada

Construction of a [[57,0,15]] quantum code:
[1]:  [[57, 0, 15]] self-dual Quantum code over GF(2^2)
     cyclic code of length 57 with generating polynomial x^51 + x^50 + x^48 + x^46 + x^41 + x^40 + x^36 + x^35 + x^34 + x^23 + x^22 + x^21 + x^17 + x^16 + x^11 + x^9 + x^7 + x^6 + 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 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 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 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 0 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1]
      [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|0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 1 0 0 1 0 1 1 0 0 1 1 1 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 1 0 0|0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 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 0 1 0|0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 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 0 1|0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 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 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 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 1 0|0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 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 1|0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 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 1 0 0|0 0 0 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1]
      [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 0|0 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 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 1|0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 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 1 0 0|0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 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 1 0|0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 0 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 0 0 0 0 1|0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 0 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 0 1 0 0|0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 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 1 0|0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 1 1 1 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 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 1|0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 1 1 1 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 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 0 0 1 0 1 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 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 0 1|0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 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 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 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 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 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 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 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 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 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 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 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 1 0|0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0]
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last modified: 2011-06-16

Notes


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