A Quadratic Form Approach to Construction A of Lattices over Cyclic\n Algebras

2020/04/03 by Grégory Berhuy, Berhuy, Grégory, Frédérique Oggier +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2004.01641

openalex publication_date 2020/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a construction of lattices from (skew-) polynomial codes, by\nendowing quotients of some ideals in both number fields and cyclic algebras\nwith a suitable trace form. We give criteria for unimodularity. This yields\nintegral and unimodular lattices with a multiplicative structure. Examples are\nprovided.\n

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