Algebraic construction of lattices via maximal quaternion orders

Author(s)

de Oliveira Benedito, Cintya Wink ^[1] ; Alves, Carina ^[2] ; Brasil Jr, Nelson Gomes ; Rodrigues Costa, Sueli Irene ^[3]

Affiliation

^[1] Sao Paulo State Univ UNESP, 505 Profa Isette Correa Fontao Ave, BR-13876750 Sao Joao Da Boa Vista, SP - Brazil

^[2] Sao Paulo State Univ UNESP, Dept Math, 1515, 24A Ave, BR-13506900 Rio Claro, SP - Brazil

^[3] Brasil Jr, Jr., Nelson Gomes, Univ Estadual Campinas, IMECC, 651 St Sergio Buarque de Holanda, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Journal of Pure and Applied Algebra; v. 224, n. 5 MAY 2020.
• Web of Science Citations: 0

Abstract

In this paper we propose a framework to construct algebraic lattices in dimensions 4n via ideals from maximal orders of a quaternion algebra whose center is a totally real number field. For n = 1,2,3,4 and 6 it was possible to construct rotated versions of the densest lattices in their dimensions, D-4, E-8, E-12, A(16) and A(24). We also present a family of lattices in dimension 2(r) from A = (-1, 1)(Q(zeta 2r + zeta 2r-1)) and a characterization of a maximal quaternion order of A by using the Chebyshev polynomials. (C) 2019 Elsevier B.V. All rights reserved. (AU)

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