Bounds on the minimum distance of additive quantum codes

Bounds on [[79,15]]2

lower bound:13
upper bound:23

Construction

Construction type: Gra

Construction of a [[79,15,13]] quantum code:
[1]:  [[85, 9, 18]] quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomials [
x^38 + w*x^37 + w*x^36 + x^35 + w*x^34 + w^2*x^32 + x^31 + w*x^30 + w^2*x^29 + x^28 + w^2*x^27 + w^2*x^26 + w*x^25 + x^24 + w^2*x^22 + w*x^21 + x^19 + x^16 + w^2*x^15 + w*x^14 + w^2*x^12 + x^11 + w*x^10 + x^9 + w^2*x^8 + x^6 + x^5 + w*x^4 + x^3 + x^2 + x + 1,
w*x^38 + w^2*x^37 + w^2*x^36 + w*x^35 + w^2*x^34 + x^32 + w*x^31 + w^2*x^30 + x^29 + w*x^28 + x^27 + x^26 + w^2*x^25 + w*x^24 + x^22 + w^2*x^21 + w*x^19 + w*x^16 + x^15 + w^2*x^14 + x^12 + w*x^11 + w^2*x^10 + w*x^9 + x^8 + w*x^6 + w*x^5 + w^2*x^4 + w*x^3 + w*x^2 + w*x + w
]
[2]:  [[80, 14, 14]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 1, 15, 67, 69, 70 }
[3]:  [[79, 15, 13]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [2] at { 80 }

    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 1 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 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 1 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 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 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0 0 1|0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1]
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      [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 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1|0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0]
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      [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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1|0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 0]
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      [0 0 0 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 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1]
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last modified: 2006-04-11

Notes


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