A quadratic form approach to Construction A of lattices over cyclic algebras - Berhuy, Grégory (2020)
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.