Bounds on the minimum distance of additive quantum codes

Bounds on [[76,1]]2

lower bound:18
upper bound:26

Construction

Construction of a [[76,1,18]] quantum code:
[1]:  [[77, 0, 19]] self-dual quantum code over GF(2^2)
     cyclic code of length 77 with generating polynomial w^2*x^76 + x^75 + w*x^74 + x^73 + w^2*x^71 + w*x^69 + w^2*x^68 + w*x^66 + w^2*x^64 + w*x^63 + w^2*x^61 + w*x^60 + w^2*x^59 + w*x^57 + w*x^54 + w*x^53 + w^2*x^52 + x^51 + w*x^50 + x^48 + x^47 + x^46 + w^2*x^45 + w*x^41 + w*x^40 + w*x^39 + w*x^38 + w*x^36 + w*x^33 + w*x^32 + 1
[2]:  [[76, 1, 18]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 77 }

    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 1|1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 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 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 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 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 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 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 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 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 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 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 1 1 0 0 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 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 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1]
      [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 1|1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 0 0 0 1 0 0 0 1 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 0 0 0 0 0 0 0 0 1|0 1 0 1 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0]
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      [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 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 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 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 1 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 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 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 1|0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 0 1]
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last modified: 2023-09-12

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014