Bounds on the minimum distance of additive quantum codes

Bounds on [[87,31]]2

lower bound:12
upper bound:19

Construction

Construction of a [[87,31,12]] quantum code:
[1]:  [[85, 33, 12]] quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomial x^84 + w^2*x^83 + w*x^82 + w^2*x^80 + w*x^79 + x^76 + x^75 + x^74 + x^73 + x^71 + w^2*x^70 + w*x^68 + w*x^66 + x^64 + w^2*x^63 + w^2*x^62 + x^60 + w^2*x^59 + w^2*x^58 + x^55 + x^54 + w*x^53 + x^52 + w^2*x^49 + x^48 + w*x^47 + w^2*x^44 + w^2*x^43 + x^42 + w^2*x^40 + w^2*x^39 + w*x^37 + w*x^36 + w^2*x^34 + x^32 + x^31 + w*x^30 + w*x^29 + w^2*x^28 + x^27 + x^26 + 1
[2]:  [[85, 31, 12]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[87, 31, 12]] quantum code over GF(2^2)
     ExtendCode [2] by 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 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0|1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 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 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0|1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 1 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