Quasi-Cyclic Subcodes of Cyclic Codes

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2017Embargo end date: 01 Jan 2016 Turkey English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Discrete Mathematics, volume 31, pages 1,454-1,475 (issn: 0895-4801, eissn: 1095-7146,

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Authors: Jean-Claude Belfiore; Cem Güneri; Buket Özkaya;

doi: 10.1137/16m1065604 , 10.48550/arxiv.1603.05063

arXiv: 1603.05063

Quasi-Cyclic Subcodes of Cyclic Codes

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Abstract

We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration is equivalent to enumeration of certain vector subspaces in finite fields. In particular, we present enumeration results for quasi-cyclic subcodes of the simplex code and duals of certain BCH codes. Our results are based on the trace representation of cyclic codes.

Country

Turkey

Related Organizations

Sabancı University
Turkey
Télécom ParisTech
France

Keywords

index, FOS: Computer and information sciences, Other types of codes, Computer Science - Information Theory, Information Theory (cs.IT), Algebraic coding theory; cryptography (number-theoretic aspects), cyclic code, quasi-cyclic code, enumeration, QA150-272.5 Algebra, Cyclic codes, subcode

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