Constructions of Dense Lattices over Number Fields

Authors

  • Antonio A. Andrade Departamento de Matemática, Ibilce - Unesp, São José do Rio Preto - SP
  • Agnaldo J. Ferrari Faculdade de Ciências, Unesp, Bauru - SP
  • José C. Interlando San Diego State University, San Diego, California
  • Robson R. Araujo Instituto Federal de São Paulo, Cubatão - SP.

DOI:

https://doi.org/10.5540/tema.2020.021.01.57

Keywords:

Algebric lattices, number fields, sphere packings.

Abstract

In this work, we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2,3,4,5,6,8 and 12, which are rotated versions of the lattices Lambda_n, for n =2,3,4,5,6,8 and K_12. These algebraic lattices are constructed through canonical homomorphism via Z-modules of the ring of algebraic integers of a number field.

Author Biographies

Antonio A. Andrade, Departamento de Matemática, Ibilce - Unesp, São José do Rio Preto - SP

Departamento de Matemática

Agnaldo J. Ferrari, Faculdade de Ciências, Unesp, Bauru - SP

Departamento de Matemática

José C. Interlando, San Diego State University, San Diego, California

Department of Mathematics and Statistic

Robson R. Araujo, Instituto Federal de São Paulo, Cubatão - SP.

Departamento de Matemática

References

A.A. Andrade and R. Palazzo Jr. Linear codes over finite rings. TEMA - Trends in Applied and Computational Mathematics, 6(2) (2005), 207-217.

A.S. Ansari, R. Shah, Zia Ur-Rahman, A.A. Andrade. Sequences of primitive and non-primitive BCH codes. TEMA - Trends in Applied and Computational Mathematics, 19(2) (2018), 369-389.

A. A. Andrade, A. J. Ferrari, C. W. O. Benedito, Constructions of algebraic lattices, Comput. Appl. Math., 29 (2010) 1-13.

E. Bayer-Fluckiger, Lattices and number fields, In: Contemp. Math., Amer. Math. Soc., Providence (1999), 69-84.

J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 3rd Edition, Springer Verlag, New York (1999).

J. C. Interlando, J. O. D. Lopes, T. P .N. Neto, The discriminant of abelian number fields, J. Algebra Appl., 5 (2006), 35-41.

P. Samuel, Algebraic Theory of Numbers, Hermann, Paris (1970).

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Published

2020-03-27

How to Cite

Andrade, A. A., Ferrari, A. J., Interlando, J. C., & Araujo, R. R. (2020). Constructions of Dense Lattices over Number Fields. Trends in Computational and Applied Mathematics, 21(1), 57. https://doi.org/10.5540/tema.2020.021.01.57

Issue

Vol. 21 No. 1 (2020)

Section

Original Article

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