Linear codes over Fq× (Fq+ vFq)

Tekkoyun M., Yaraneri E.

Journal of Applied Mathematics and Computing, vol.69, no.4, pp.3553-3578, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.1007/s12190-023-01893-5
  • Journal Name: Journal of Applied Mathematics and Computing
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.3553-3578
  • Keywords: Codes over rings, Cyclic codes, Dual codes, Free codes, Linear codes
  • Istanbul Technical University Affiliated: Yes

Abstract

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.