Bounds on the minimum distance of additive quantum codes

Bounds on [[81,10]]2

lower bound:15
upper bound:25

Construction

Construction of a [[81,10,15]] quantum code:
[1]:  [[85, 9, 19]] quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomial x^38 + w*x^37 + w*x^36 + w^2*x^35 + w*x^34 + x^33 + w^2*x^30 + x^29 + w*x^28 + x^26 + w*x^25 + w*x^22 + w*x^21 + w*x^19 + w^2*x^18 + w^2*x^16 + x^14 + x^13 + w*x^10 + x^8 + x^6 + x^5 + w*x^4 + w^2*x^3 + 1
[2]:  [[81, 13, 15]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 82 .. 85 }
[3]:  [[81, 10, 15]] quantum code over GF(2^2)
     Subcode of [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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 1|0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 0 0 1 0 1 0 1 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 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 0|0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0]
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last modified: 2015-05-28

Notes


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