Bounds on the minimum distance of additive quantum codes

Bounds on [[83,20]]2

lower bound:13
upper bound:22

Construction

Construction of a [[83,20,13]] quantum code:
[1]:  [[85, 21, 15]] quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomial x^82 + x^81 + x^80 + w^2*x^79 + x^78 + w*x^77 + w^2*x^76 + x^74 + w*x^73 + w*x^72 + w^2*x^71 + w^2*x^69 + w^2*x^68 + x^67 + w*x^66 + w*x^65 + w*x^64 + w*x^63 + x^61 + x^60 + w*x^59 + x^58 + w^2*x^56 + x^55 + w*x^54 + w^2*x^52 + w^2*x^48 + w^2*x^47 + w*x^46 + w*x^45 + w*x^44 + w^2*x^43 + w^2*x^42 + w*x^41 + x^40 + w^2*x^39 + x^38 + w*x^37 + x^36 + x^35 + w*x^34 + w*x^33 + x^32 + 1
[2]:  [[83, 23, 13]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 84, 85 }
[3]:  [[83, 20, 13]] quantum code over GF(2^2)
     Subcode of [2]

    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 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1|0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 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 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0|1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0]
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      [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 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0|0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 1 0]
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last modified: 2006-04-03

Notes


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