Constacyclic locally recoverable codes from their duals

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dc.authoridKÖROĞLU, Mehmet Emin/0000-0002-9173-4944
dc.authorwosidKÖROĞLU, Mehmet Emin/P-7940-2015
dc.contributor.authorZengin, Rabia
dc.contributor.authorKoroglu, Mehmet Emin
dc.date.accessioned2024-07-18T20:42:24Z
dc.date.available2024-07-18T20:42:24Z
dc.date.issued2024
dc.departmentİstanbul Bilgi Üniversitesien_US
dc.description.abstractA code has locality r if a symbol in any coordinate of a codeword in the code can be recovered by accessing the value of at most r other coordinates. Such codes are called locally recoverable codes (LRCs for short). Since LRCs can recover a failed node by accessing the minimum number of the surviving nodes, these codes are used in distributed storage systems such as Microsoft Azure. In this paper, constacyclic LRCs are obtained from their parity-check polynomials. Constacyclic codes with locality r <= 2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r\le 2$$\end{document} and dimension 2 are obtained and a sufficient and necessary condition for these codes to have locality 1 is given. Then, the construction is generalized. Distance optimal constacyclic LRCs with distance 2 are obtained. Also, constacyclic codes with locality 1 are constructed. They may be so useful in practice thanks to their minimum locality. Constacyclic codes whose locality is equal to their dimension are given. Furthermore, constacyclic LRCs are obtained from cyclotomic cosets.en_US
dc.description.sponsorshipYildiz Technical University Scientific Research Projects Coordination Department [FYL-2023-5605]; Scientific and Technological Research Council of Turkiye (TUBITAK) [BIDEB-2210]en_US
dc.description.sponsorshipThis research was supported by the Yildiz Technical University Scientific Research Projects Coordination Department (Project Number: FYL-2023-5605) and first author is partially supported by the Scientific and Technological Research Council of Turkiye (TUBITAK) (Grant Number: BIDEB-2210). The authors would like to thank the editors and the referees for their constructive comments, which have greatly contributed to improving the paper.en_US
dc.identifier.doi10.1007/s40314-024-02705-7
dc.identifier.issn2238-3603
dc.identifier.issn1807-0302
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-85190655329en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.urihttps://doi.org/10.1007/s40314-024-02705-7
dc.identifier.urihttps://hdl.handle.net/11411/7271
dc.identifier.volume43en_US
dc.identifier.wosWOS:001205111400001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringer Heidelbergen_US
dc.relation.ispartofComputational & Applied Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectLocally Recoverable Codesen_US
dc.subjectConstacyclic Codesen_US
dc.subjectCyclotomic Cosetsen_US
dc.subjectOptimalityen_US
dc.subjectRepairable Codesen_US
dc.subjectDistance 5en_US
dc.subjectConstructionsen_US
dc.subjectBinaryen_US
dc.subjectBoundsen_US
dc.titleConstacyclic locally recoverable codes from their duals
dc.typeArticle

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