Crossed Products and Coding Theory

Yuval Ginosar; Aviram Rochas Moreno

doi:10.1109/TIT.2019.2923652

Crossed Products and Coding Theory

Yuval Ginosar, Aviram Rochas Moreno

Department of Mathematics

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

Abstract

Families of codes, such as group codes, constacyclic, and skew cyclic codes, which were independently suggested, turn out to be special instances of the general family of crossed product codes. Under this framework, the ambient code spaces are classified here with respect to Hamming-isometry in cohomological terms. This classification is demonstrated by two families of examples. We also determine when crossed products belonging to these families are semisimple and, in particular, when they admit only trivial codes.

Original language	English
Article number	8741079
Pages (from-to)	6224-6233
Number of pages	10
Journal	IEEE Transactions on Information Theory
Volume	65
Issue number	10
DOIs	https://doi.org/10.1109/TIT.2019.2923652
State	Published - Oct 2019

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

Crossed products
Hamming isometry
completion property
skew-constacyclic codes
twisted elementary Abelian codes

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

Access to Document

10.1109/TIT.2019.2923652

Cite this

@article{3ddf7c806124416dba3492523009023a,

title = "Crossed Products and Coding Theory",

abstract = "Families of codes, such as group codes, constacyclic, and skew cyclic codes, which were independently suggested, turn out to be special instances of the general family of crossed product codes. Under this framework, the ambient code spaces are classified here with respect to Hamming-isometry in cohomological terms. This classification is demonstrated by two families of examples. We also determine when crossed products belonging to these families are semisimple and, in particular, when they admit only trivial codes.",

keywords = "Crossed products, Hamming isometry, completion property, skew-constacyclic codes, twisted elementary Abelian codes",

author = "Yuval Ginosar and {Rochas Moreno}, Aviram",

note = "Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2019",

month = oct,

doi = "10.1109/TIT.2019.2923652",

language = "English",

volume = "65",

pages = "6224--6233",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "10",

}

TY - JOUR

T1 - Crossed Products and Coding Theory

AU - Ginosar, Yuval

AU - Rochas Moreno, Aviram

PY - 2019/10

Y1 - 2019/10

N2 - Families of codes, such as group codes, constacyclic, and skew cyclic codes, which were independently suggested, turn out to be special instances of the general family of crossed product codes. Under this framework, the ambient code spaces are classified here with respect to Hamming-isometry in cohomological terms. This classification is demonstrated by two families of examples. We also determine when crossed products belonging to these families are semisimple and, in particular, when they admit only trivial codes.

AB - Families of codes, such as group codes, constacyclic, and skew cyclic codes, which were independently suggested, turn out to be special instances of the general family of crossed product codes. Under this framework, the ambient code spaces are classified here with respect to Hamming-isometry in cohomological terms. This classification is demonstrated by two families of examples. We also determine when crossed products belonging to these families are semisimple and, in particular, when they admit only trivial codes.

KW - Crossed products

KW - Hamming isometry

KW - completion property

KW - skew-constacyclic codes

KW - twisted elementary Abelian codes

UR - http://www.scopus.com/inward/record.url?scp=85077399339&partnerID=8YFLogxK

U2 - 10.1109/TIT.2019.2923652

DO - 10.1109/TIT.2019.2923652

M3 - Article

AN - SCOPUS:85077399339

SN - 0018-9448

VL - 65

SP - 6224

EP - 6233

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 10

M1 - 8741079

ER -

Crossed Products and Coding Theory

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this