A Quadratic Form Approach to Construction A of Lattices over Cyclic Algebras (2004.01641v1)

Abstract: We propose a construction of lattices from (skew-) polynomial codes, by endowing quotients of some ideals in both number fields and cyclic algebras with a suitable trace form. We give criteria for unimodularity. This yields integral and unimodular lattices with a multiplicative structure. Examples are provided.