Bounds on the minimum distance of additive quantum codes

Bounds on [[69,8]]2

lower bound:14
upper bound:22

Construction

Construction type: Grassl

Construction of a [[69,8,14]] quantum code:
[1]:  [[68, 8, 14]] quantum code over GF(2^2)
     QuasiCyclicCode of length 68 with generating polynomials: w^2*x^32 + x^31 + x^30 + x^4,  w^2*x^33 + x^31 + w^2*x^30 + w*x^27 + x^25 + w*x^24 + w*x^23 + x^22 + w*x^21 + w*x^20 + x^18 + x^17 + x^16 + w^2*x^15 + w*x^14 + w^2*x^13 + x^12 + x^10 + w*x^9 + w*x^8 + x^7 + x^5 + w^2*x^4 + x^3 + w^2*x^2 + w^2
[2]:  [[69, 8, 14]] quantum code over GF(2^2)
     ExtendCode [1] by 1

    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 1 0 0 0 1 1 0 0 0 0 0|0 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 1 1 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 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0|0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0]
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last modified: 2011-07-09

Notes


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