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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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

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spelling	sg-ntu-dr.10356-1443352023-02-28T19:56:51Z A quadratic form approach to Construction A of lattices over cyclic algebras Berhuy, Grégory Oggier, Frédérique School of Physical and Mathematical Sciences Science::Mathematics::Algebra Construction A Cyclic Algebra 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. Accepted version 2020-10-29T04:08:06Z 2020-10-29T04:08:06Z 2021 Journal Article Berhuy, G., & Oggier, F. (2021). A quadratic form approach to Construction A of lattices over cyclic algebras. Journal of Pure and Applied Algebra, 225(6), 106600-. doi:10.1016/j.jpaa.2020.106600 0022-4049 https://hdl.handle.net/10356/144335 10.1016/j.jpaa.2020.106600 6 225 106600 en Journal of Pure and Applied Algebra © 2020 Elsevier B.V. All rights reserved.This paper was published in Journal of Pure and Applied Algebra and is made available with permission of Elsevier B.V. application/pdf
institution	Nanyang Technological University
building	NTU Library
continent	Asia
country	Singapore Singapore
content_provider	NTU Library
collection	DR-NTU
language	English
topic	Science::Mathematics::Algebra Construction A Cyclic Algebra
spellingShingle	Science::Mathematics::Algebra Construction A Cyclic Algebra Berhuy, Grégory Oggier, Frédérique A quadratic form approach to Construction A of lattices over cyclic algebras
description	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.
author2	School of Physical and Mathematical Sciences
author_facet	School of Physical and Mathematical Sciences Berhuy, Grégory Oggier, Frédérique
format	Article
author	Berhuy, Grégory Oggier, Frédérique
author_sort	Berhuy, Grégory
title	A quadratic form approach to Construction A of lattices over cyclic algebras
title_short	A quadratic form approach to Construction A of lattices over cyclic algebras
title_full	A quadratic form approach to Construction A of lattices over cyclic algebras
title_fullStr	A quadratic form approach to Construction A of lattices over cyclic algebras
title_full_unstemmed	A quadratic form approach to Construction A of lattices over cyclic algebras
title_sort	quadratic form approach to construction a of lattices over cyclic algebras
publishDate	2020
url	https://hdl.handle.net/10356/144335
_version_	1759857266618531840

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

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