Bounds on the minimum distance of additive quantum codes

Bounds on [[63,0]]2

lower bound:16
upper bound:22

Construction

Construction type: Harada

Construction of a [[63,0,16]] quantum code:
[1]:  [[63, 0, 16]] self-dual Quantum code over GF(2^2)
     cyclic code of length 63 with generating polynomial x^62 + x^59 + x^58 + x^55 + x^51 + x^50 + x^49 + x^48 + x^47 + x^45 + x^18 + x^16 + x^15 + x^14 + x^13 + x^12 + x^8 + x^5 + x^4 + 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 0 0 0 0 0 0 0 0 1|0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 1|0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 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 0 0 0 0 0 0 0 0 0 1|0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 1|0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 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 0 0 0 0 0 0 0 1|0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 1 0 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 0 0 0 0 0 0 1|0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 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 0 0 0 0 0 1|0 1 1 1 1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1]
      [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 1|0 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 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 0 0 0 0 0 0 1|0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 1|0 0 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 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 0 0 0 0 0 0 0 1|0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 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 1|0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 0 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 1|0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 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 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|0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 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 1|0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 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 1|0 1 1 1 1 0 0 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 1 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 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 1 1 0 0 1 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 0 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 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 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 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 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 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 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 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 1 0 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 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 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 1|0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 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 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 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1]
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last modified: 2011-06-18

Notes


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