Bounds on the minimum distance of additive quantum codes

Bounds on [[103,17]]2

lower bound:18
upper bound:29

Construction

Construction of a [[103,17,18]] quantum code:
[1]:  [[105, 15, 20]] quantum code over GF(2^2)
     constacyclic code generated by x^104 + w^2*x^103 + x^102 + x^100 + w*x^97 + w^2*x^96 + x^94 + x^93 + x^90 + w*x^89 + w*x^88 + w*x^87 + x^86 + x^84 + w*x^82 + x^80 + w^2*x^79 + x^78 + x^76 + x^73 + w*x^69 + w*x^64 + x^62 + w^2*x^61 + w^2*x^60 + x^42 with shift constant w
[2]:  [[103, 17, 18]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 104 .. 105 }

    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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1|1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 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 1 1 0 1 0 1 0 0 1 0|1 0 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0]
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last modified: 2020-08-31

Notes


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