Algebraic constructions of densest lattices

作     者：Jorge, Grasiele C. de Andrade, Antonio A. Costa, Sueli I. R. Strapasson, Joao E. 

作者机构：Univ Fed Sao Paulo UNIFESP BR-12247014 Sao Jose Dos Campos SP Brazil Sao Paulo State Univ UNESP BR-15054000 Sao Jose Do Rio Preto SP Brazil Univ Estadual Campinas UNICAMP BR-13083859 Campinas SP Brazil Univ Estadual Campinas UNICAMP BR-13484350 Limeira SP Brazil 

出 版 物：《JOURNAL OF ALGEBRA》 (代数杂志)

年 卷 期：2015年第429卷

页      面：218-235页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：CNPq [150802/2012-9, 312926/2013-8] FAPESP [2013/25977-7] Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) [13/25977-7] Funding Source: FAPESP 

主　　题：Algebraic number theory Lattices Packing density Diversity Minimum product distance Coding theory 

摘      要：The aim of this paper is to investigate rotated versions of the densest known lattices in dimensions 2, 3, 4, 5, 6, 7, 8, 12 and 24 constructed via ideals and free Z-modules that are not ideals in subfields of cyclotomic fields. The focus is on totally real number fields and the associated full diversity lattices which may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. We also discuss on the existence of a number field K such that it is possible to obtain the lattices A(2), E-6 and E-7 via a twisted embedding applied to a fractional ideal of O-K. (C) 2015 Elsevier Inc. All rights reserved.