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Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes
Date
2022-03-01
Author
Koese, Seyda
Özbudak, Ferruh
Metadata
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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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.
Subject Keywords
Polynomial factorization
,
Finite local commutative ring
,
Self-dual codes
,
LCD codes
,
Quasi twisted codes
,
QUASI-TWISTED CODES
,
SIDE-CHANNEL
URI
https://hdl.handle.net/11511/96945
Journal
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
DOI
https://doi.org/10.1007/s12095-022-00557-8
Collections
Department of Mathematics, Article
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S. Koese and F. Özbudak, “Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes,”
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/96945.