Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes

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Koese S., ÖZBUDAK F.

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, vol.14, no.4, pp.933-948, 2022 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 14 Issue: 4
• Publication Date: 2022
• Doi Number: 10.1007/s12095-022-00557-8
• Journal Name: CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
• Page Numbers: pp.933-948
• Keywords: Polynomial factorization, Finite local commutative ring, Self-dual codes, LCD codes, Quasi twisted codes, QUASI-TWISTED CODES, SIDE-CHANNEL
• Middle East Technical University Affiliated: Yes

Abstract

We determine the unique factorization of some polynomials over a finite local commutative ring with identity explicitly. This solves and generalizes the main conjecture of Qian, Shi and Sole in [13]. We also give some applications to enumeration of certain generalized double circulant self-dual and linear complementary dual (LCD) codes over some finite rings together with an application in asymptotic coding theory.