On projections of arbitrary lattices

Author(s)

Campello, Antonio ^[1] ; Strapasson, Joao ^[2] ; Costa, Sueli I. R. ^[1]

Affiliation

^[1] Univ Estadual Campinas, Inst Math Stat & Comp Sci, BR-13083859 Campinas, SP - Brazil

^[2] Univ Estadual Campinas, Sch Appl Sci, BR-13484350 Limeira, SP - Brazil

• Document type: Journal article
• Source: Linear Algebra and its Applications; v. 439, n. 9, p. 2577-2583, NOV 1 2013.
• Web of Science Citations: 1

Abstract

In this paper we prove that given any two point lattices Lambda(1) subset of R-n and Lambda(2) subset of Rn-k, there is a set of k vectors [v(1), ..., v(k)) subset of Lambda(1) such that Lambda(2) is, up to similarity, arbitrarily close to the projection of Lambda(1) onto the orthogonal complement of the subspace spanned by [v(1), ..., v(k)]. This result extends the main theorem of Sloane et al. (2011) {[}1] and has applications in communication theory. (C) 2013 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 11/22044-4 - Lattices and codes: perspectives in cryptography
• Grantee: Antonio Carlos de Andrade Campello Junior
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• FAPESP's process: 11/01096-6 - Discrete mathematics: lattices, codes and cryptography
• Grantee: João Eloir Strapasson
• Support Opportunities: Regular Research Grants