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

Grégory Berhuy; Frédérique Oggier

doi:10.1016/j.jpaa.2020.106600

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

Grégory Berhuy
, Frédérique Oggier^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	106600
Number of pages	35
Journal	Journal of Pure and Applied Algebra
Volume	225
Issue number	6
Early online date	14 Oct 2020
DOIs	https://doi.org/10.1016/j.jpaa.2020.106600
Publication status	Published - Jun 2021

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

Construction A
Cyclic algebra
Integral lattices
Linear codes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2020.106600Licence: None: All rights reserved

Cite this

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title = "A quadratic form approach to Construction A of lattices over cyclic algebras",

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.",

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AU - Oggier, Frédérique

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AB - 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.

KW - Construction A

KW - Cyclic algebra

KW - Integral lattices

KW - Linear codes

UR - https://www.scopus.com/pages/publications/85093654408

U2 - 10.1016/j.jpaa.2020.106600

DO - 10.1016/j.jpaa.2020.106600

M3 - Article

AN - SCOPUS:85093654408

SN - 0022-4049

VL - 225

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 6

M1 - 106600

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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