Bounds on the minimum distance of additive quantum codes

Bounds on [[78,7]]2

lower bound:15
upper bound:25

Construction

Construction of a [[78,7,15]] quantum code:
[1]:  [[75, 8, 15]] quantum code over GF(2^2)
     cyclic code of length 75 with generating polynomial x^74 + w*x^73 + w^2*x^72 + w^2*x^71 + w^2*x^70 + w*x^69 + w*x^68 + x^67 + x^66 + w*x^62 + w^2*x^61 + w*x^60 + w*x^59 + w^2*x^58 + x^57 + w*x^56 + w^2*x^55 + w*x^53 + w*x^52 + w^2*x^51 + w^2*x^49 + w^2*x^48 + w*x^47 + w*x^45 + x^44 + w*x^43 + w*x^42 + w*x^40 + w^2*x^39 + x^38 + w*x^37 + x^36 + w*x^35 + x^34 + 1
[2]:  [[75, 7, 15]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[78, 7, 15]] quantum code over GF(2^2)
     ExtendCode [2] by 3

    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 1 0 1 1 0 0 0|0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0]
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last modified: 2008-02-16

Notes


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