A quadratic form approach to Construction A of lattices over cyclic algebras

A quadratic form approach to Construction A of lattices over cyclic algebras

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. Example...

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Bibliographic Details
Main Authors: Berhuy, Grégory, Oggier, Frédérique
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2020
Subjects:
Science::Mathematics::Algebra
Construction A
Cyclic Algebra
Online Access:https://hdl.handle.net/10356/144335
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Institution: Nanyang Technological University
Language: English
Description
Summary: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.

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