Bounds on the minimum distance of additive quantum codes

Bounds on [[119,75]]2

lower bound:8
upper bound:14

Construction

Construction of a [[119,75,8]] quantum code:
[1]:  [[111, 75, 8]] quantum code over GF(2^2)
     constacyclic code generated by w*x^110 + w^2*x^109 + w^2*x^108 + w^2*x^107 + w^2*x^106 + w*x^105 + x^104 + w^2*x^102 + w*x^101 + x^97 + w^2*x^96 + w^2*x^95 + w^2*x^92 + w^2*x^91 + x^90 + x^87 + x^85 + w^2*x^84 + x^83 + x^82 + w^2*x^81 + w^2*x^80 + w*x^79 + w*x^78 + x^77 + w^2*x^76 + w^2*x^75 + w*x^74 + w*x^73 + w*x^72 + w*x^71 + x^70 + x^69 + w^2*x^68 + x^67 + w*x^65 + w^2*x^64 + x^63 + x^59 + x^58 + w*x^57 + w*x^55 + x^54 + w^2*x^53 + w*x^51 + w*x^48 + x^46 + x^45 + w*x^44 + w^2*x^43 + w^2*x^41 + w*x^40 + w^2*x^38 + w*x^37 + w^2*x^36 + w*x^35 + x^34 + x^33 + w^2*x^32 + w*x^31 + w^2*x^30 + w^2*x^29 + w*x^28 + w*x^26 + w*x^25 + x^22 + w*x^21 + w^2*x^19 + x^18 + 1 with shift constant w^2
[2]:  [[119, 75, 8]] quantum code over GF(2^2)
     ExtendCode [1] by 8

    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 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0|1 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 1 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 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0|1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0 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