Bounds on the minimum distance of additive quantum codes

Bounds on [[78,1]]2

lower bound:18
upper bound:27

Construction

Construction of a [[78,1,18]] quantum code:
[1]:  [[79, 0, 19]] self-dual quantum code over GF(2^2)
     cyclic code of length 79 with generating polynomial x^78 + x^76 + x^73 + x^70 + x^67 + x^65 + x^62 + x^61 + x^60 + x^59 + x^57 + x^56 + x^55 + x^51 + x^50 + x^49 + x^48 + x^45 + x^44 + x^43 + x^41 + x^38 + x^36 + x^35 + x^34 + x^31 + x^30 + x^29 + x^28 + x^24 + x^23 + x^22 + x^20 + x^19 + x^18 + x^17 + x^14 + x^12 + x^9 + x^6 + x^3 + x + w
[2]:  [[78, 1, 18]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at 79

    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 1|0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 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 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 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 1 1 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 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 0 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1]
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last modified: 2011-06-21

Notes


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