Crossed Products and Coding Theory

Yuval Ginosar; Aviram Rochas Moreno

doi:https://doi.org/10.1109/TIT.2019.2923652

Crossed Products and Coding Theory

Yuval Ginosar, Aviram Rochas Moreno

Department of Mathematics

University of Haifa

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	American 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

Keywords

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

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

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https://doi.org/10.1109/TIT.2019.2923652

Cite this

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

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

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year = "2019",

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KW - Crossed products

KW - Hamming isometry

KW - completion property

KW - skew-constacyclic codes

KW - twisted elementary Abelian codes

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ER -

Crossed Products and Coding Theory

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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