Bounds on the minimum distance of additive quantum codes

Bounds on [[77,19]]2

lower bound:12
upper bound:21

Construction

Construction of a [[77,19,12]] quantum code:
[1]:  [[73, 19, 12]] quantum code over GF(2^2)
     cyclic code of length 73 with generating polynomial x^72 + x^71 + x^70 + w*x^69 + w^2*x^68 + w*x^67 + x^66 + w*x^65 + w^2*x^64 + w^2*x^63 + x^62 + x^61 + x^60 + w^2*x^59 + x^58 + w^2*x^57 + x^56 + w^2*x^52 + w*x^49 + w^2*x^47 + w*x^46 + x^45 + w^2*x^44 + x^43 + w*x^42 + x^41 + w^2*x^40 + w^2*x^38 + w^2*x^37 + w^2*x^35 + w*x^33 + w*x^32 + w^2*x^30 + w^2*x^29 + x^27 + x^26 + x^25 + 1
[2]:  [[77, 19, 12]] quantum code over GF(2^2)
     ExtendCode [1] by 4

    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 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0|1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 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 1 0 1 1 0 1 1 0 1 0 0 1 1 1 0 1 0 1 0 0 0 0 0|0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 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 1 0 1 1 0 1 1 0 1 0 0 1 1 1 0 1 0 1 0 0 0 0|1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0]
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      [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 1 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 0 0 0 0|1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0]
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last modified: 2008-02-16

Notes


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