Author(s): Ferrari, Agnaldo José [UNESP] ; de Andrade, Antonio Aparecido [UNESP] ; de Araujo, Robson Ricardo ; Interlando, José Carmelo
Date: 2020
Persistent ID: http://hdl.handle.net/11449/200639
Origin: Oasisbr
Subject(s): Algebraic lattices; Cyclotomic fields; Signal design; Twisted homomorphism; Algebraic lattices; Algebraic lattices; Cyclotomic fields; Cyclotomic fields; Signal design; Signal design; Twisted homomorphism; Twisted homomorphism
Made available in DSpace on 2020-12-12T02:12:06Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-05-07
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
In this work, we present a explicit trace forms for maximal real subfields of cyclotomic fields as tools for constructing algebraic lattices in Euclidean space with optimal center density. We also obtain a closed formula for the Gram matrix of algebraic lattices obtained from these subfields. The obtained lattices are rotated versions of the lattices Λ9, Λ10 and Λ11 and they are images of Z-submodules of rings of integers under the twisted homomorphism, and these constructions, as algebraic lattices, are new in the literature. We also obtain algebraic lattices in odd dimensions up to 7 over real subfields, calculate their minimum product distance and compare with those known in literatura, since lattices constructed over real subfields have full diversity.
Department of Mathematics School of Sciences São Paulo State University (Unesp)
Department of Mathematics Institute of Biosciences Humanities and Exact Sciences (Ibilce) São Paulo State University (Unesp)
São Paulo Federal Institute at Cubatão
Department of Mathematics & Statistics San Diego University
Department of Mathematics School of Sciences São Paulo State University (Unesp)
Department of Mathematics Institute of Biosciences Humanities and Exact Sciences (Ibilce) São Paulo State University (Unesp)
CNPq: 429346/2018-2
