Linear codes over Fq× (Fq+ vFq)

Mevlüt Tekkoyun; Ergün Yaraneri

doi:10.1007/s12190-023-01893-5

Linear codes over F_q× (F_q+ vF_q)

Mevlüt Tekkoyun^*, Ergün Yaraneri

^*Corresponding author for this work

Department of Mathematics Engineering

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

1 Citation (Scopus)

Abstract

Let R be the F_q -algebra F_q× (F_q+ vF_q) of order q³ where v²= v and F_q is a finite field of q elements. We study linear codes over R, not only generalizing most of the existing results for q= 2 but also adding some new results. Our work is quite comprehensive including standard forms of generator matrices, free codes, dual codes, cyclic codes.

Original language	English
Pages (from-to)	3553-3578
Number of pages	26
Journal	Journal of Applied Mathematics and Computing
Volume	69
Issue number	4
DOIs	https://doi.org/10.1007/s12190-023-01893-5
Publication status	Published - Aug 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics.

Keywords

Codes over rings
Cyclic codes
Dual codes
Free codes
Linear codes

Access to Document

10.1007/s12190-023-01893-5

Cite this

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N2 - Let R be the Fq -algebra Fq× (Fq+ vFq) of order q3 where v2= v and Fq is a finite field of q elements. We study linear codes over R, not only generalizing most of the existing results for q= 2 but also adding some new results. Our work is quite comprehensive including standard forms of generator matrices, free codes, dual codes, cyclic codes.

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KW - Codes over rings

KW - Cyclic codes

KW - Dual codes

KW - Free codes

KW - Linear codes

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