Construção de Códigos Esféricos através do Reticulado Hexagonal

Authors

  • C. Alves
  • A.A. de Andrade
  • S.I.R. Costa

DOI:

https://doi.org/10.5540/tema.2010.011.01.0001

Abstract

Códigos esféricos n-dimensionais gerados por grupos comutativos em dimensão par, n = 2m, podem ser determinados pelo quociente de reticulados m-dimensionais, quando os vetores que geram o sub-reticulado são mutuamente ortogonais [4]. Apresentamos a construção de sub-reticulados nestas condições, a partir do reticulado hexagonal, A2. Comparamos a distância mínima do código esférico construído através do quociente destes reticulados com o limitante da distância mínima estabelecido em [5].

References

[1] C. Alves, “Reticulados e Códigos”, Tese de Doutorado, IMECC-Unicamp, 2008.

E. Biglieri, M. Elia, Cyclic-group codes for the Gaussian channel, IEEE Transactions on Information Theory, 22 (1976), 624-629.

H.C. Cohen, “A Course in Computational Algebraic Number Theory”, Springer-Verlag, New York, 1993.

S.I.R. Costa, M. Muniz, E. Augustini, R. Palazzo, Graphs, tessellations and perfect codes on flat tori, IEEE Transactions on Information Theory, 50 (2004), 2363–2377.

R.M. Siqueira, S.I.R. Costa, Flat tori, lattices and bounds for commutative group codes, Designs, Codes and Cryptography, 49 (2008), 307–321.

D. Slepian, Group codes for the Gaussian channel, Bell Syst. Tech. Journal, 47 (1968), 575–602.

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Published

2010-06-01

How to Cite

Alves, C., Andrade, A. de, & Costa, S. (2010). Construção de Códigos Esféricos através do Reticulado Hexagonal. Trends in Computational and Applied Mathematics, 11(1), 1–8. https://doi.org/10.5540/tema.2010.011.01.0001

Issue

Vol. 11 No. 1 (2010)

Section

Original Article

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