Bounds on the minimum distance of additive quantum codes

Bounds on [[104,1]]2

lower bound:21
upper bound:35

Construction

Construction of a [[104,1,21]] quantum code:
[1]:  [[101, 1, 21]] quantum code over GF(2^2)
     cyclic code of length 101 with generating polynomials [
w^2*x^100 + w^2*x^99 + x^98 + w*x^96 + x^95 + x^94 + w^2*x^93 + w^2*x^92 + w^2*x^91 + w^2*x^89 + w^2*x^87 + w^2*x^85 + w^2*x^84 + w*x^82 + x^81 + x^79 + w*x^78 + x^77 + x^76 + x^75 + x^74 + w*x^73 + x^72 + x^70 + w*x^69 + w^2*x^67 + w^2*x^66 + w^2*x^64 + w^2*x^62 + w^2*x^60 + w^2*x^59 + w^2*x^58 + x^57 + x^56 + w*x^55 + x^53 + w^2*x^52 + w^2*x^51 + x^50 + 1,
x^100 + x^99 + w*x^98 + w^2*x^96 + w*x^95 + w*x^94 + x^93 + x^92 + x^91 + x^89 + x^87 + x^85 + x^84 + w^2*x^82 + w*x^81 + w*x^79 + w^2*x^78 + w*x^77 + w*x^76 + w*x^75 + w*x^74 + w^2*x^73 + w*x^72 + w*x^70 + w^2*x^69 + x^67 + x^66 + x^64 + x^62 + x^60 + x^59 + x^58 + w*x^57 + w*x^56 + w^2*x^55 + w*x^53 + x^52 + x^51 + w*x^50 + w
]
[2]:  [[104, 1, 21]] quantum code over GF(2^2)
     ExtendCode [1] 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 0 0 0 0 0 0 0 0 0 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 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 0]
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last modified: 2006-04-07

Notes


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