Maximal order codes over number fields

Christian Maire; Frédérique Oggier

doi:10.1016/j.jpaa.2017.08.009

Maximal order codes over number fields

Christian Maire, Frédérique Oggier^*

^*Corresponding author for this work

Mathematics

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

Abstract

We present constructions of codes obtained from maximal orders over number fields. Particular cases include codes from algebraic number fields by Lenstra and Guruswami, codes from units of the ring of integers of number fields, and codes from both additive and multiplicative structures of maximal orders in central simple division algebras. The parameters of interest are the code rate and the minimum Hamming distance. An asymptotic study reveals several families of asymptotically good codes.

Original language	English
Pages (from-to)	1827-1858
Number of pages	32
Journal	Journal of Pure and Applied Algebra
Volume	222
Issue number	7
DOIs	https://doi.org/10.1016/j.jpaa.2017.08.009
Publication status	Published - Jul 2018

Bibliographical note

Publisher Copyright:
© 2017 Elsevier B.V.

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jpaa.2017.08.009

Cite this

@article{a21d097e52a54199950d9e79a8ea0454,

title = "Maximal order codes over number fields",

abstract = "We present constructions of codes obtained from maximal orders over number fields. Particular cases include codes from algebraic number fields by Lenstra and Guruswami, codes from units of the ring of integers of number fields, and codes from both additive and multiplicative structures of maximal orders in central simple division algebras. The parameters of interest are the code rate and the minimum Hamming distance. An asymptotic study reveals several families of asymptotically good codes.",

author = "Christian Maire and Fr{\'e}d{\'e}rique Oggier",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2018",

month = jul,

doi = "10.1016/j.jpaa.2017.08.009",

language = "English",

volume = "222",

pages = "1827--1858",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier",

number = "7",

}

TY - JOUR

T1 - Maximal order codes over number fields

AU - Maire, Christian

AU - Oggier, Frédérique

PY - 2018/7

Y1 - 2018/7

N2 - We present constructions of codes obtained from maximal orders over number fields. Particular cases include codes from algebraic number fields by Lenstra and Guruswami, codes from units of the ring of integers of number fields, and codes from both additive and multiplicative structures of maximal orders in central simple division algebras. The parameters of interest are the code rate and the minimum Hamming distance. An asymptotic study reveals several families of asymptotically good codes.

AB - We present constructions of codes obtained from maximal orders over number fields. Particular cases include codes from algebraic number fields by Lenstra and Guruswami, codes from units of the ring of integers of number fields, and codes from both additive and multiplicative structures of maximal orders in central simple division algebras. The parameters of interest are the code rate and the minimum Hamming distance. An asymptotic study reveals several families of asymptotically good codes.

UR - http://www.scopus.com/inward/record.url?scp=85044391503&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2017.08.009

DO - 10.1016/j.jpaa.2017.08.009

M3 - Article

AN - SCOPUS:85044391503

SN - 0022-4049

VL - 222

SP - 1827

EP - 1858

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 7

ER -

Maximal order codes over number fields

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this