Well-rounded algebraic lattices in odd prime dimension

Author(s)

de Araujo, Robson R. ^[1] ; Costa, Sueli I. R. ^[1]

Affiliation

^[1] Univ Estadual Campinas, Inst Math, Rua Sergio Buarque de Holanda 561, Campinas, SP - Brazil

• Document type: Journal article
• Source: ARCHIV DER MATHEMATIK; v. 112, n. 2, p. 139-148, FEB 2019.
• Web of Science Citations: 0

Abstract

Well-rounded lattices have been considered in coding theory, in approaches to MIMO, and SISO wiretap channels. Algebraic lattices have been used to obtain dense lattices and in applications to Rayleigh fading channels. Recent works study the relation between well-rounded lattices and algebraic lattices, mainly in dimension two. In this article we present a construction of well-rounded algebraic lattices in Euclidean spaces of odd prime dimension. We prove that for each Abelian number field of odd prime degree having squarefree conductor, there exists a Z-module M such that the canonical embedding applied to M produces a well-rounded lattice. It is also shown that for each odd prime dimension there are infinitely many non-equivalent well-rounded algebraic lattices, with high indexes as sublattices of other algebraic lattices. (AU)

• FAPESP's process: 13/25977-7 - Security and reliability of Information: theory and practice
• Grantee: Marcelo Firer
• Support Opportunities: Research Projects - Thematic Grants