Bounds on the minimum distance of additive quantum codes

Bounds on [[89,37]]2

lower bound:11
upper bound:18

Construction

Construction of a [[89,37,11]] quantum code:
[1]:  [[85, 37, 11]] quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomial w*x^83 + w^2*x^82 + w*x^81 + w^2*x^80 + w*x^77 + w*x^75 + w^2*x^74 + w^2*x^73 + x^72 + w^2*x^71 + w^2*x^70 + x^69 + x^67 + x^66 + w*x^65 + w^2*x^63 + x^62 + x^61 + w^2*x^60 + w*x^59 + w^2*x^58 + w*x^57 + w*x^56 + w^2*x^55 + x^54 + w^2*x^53 + w*x^51 + w*x^49 + w*x^48 + w^2*x^46 + w^2*x^45 + x^43 + w*x^40 + x^39 + w^2*x^38 + x^37 + w^2*x^36 + x^35 + w*x^33 + w^2*x^31 + x^30 + w^2*x^29 + w^2*x^27 + w*x^26 + x^24 + 1
[2]:  [[89, 37, 11]] 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 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0|0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 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 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0|1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 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