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

Köse S, Özbudak F. 2022. Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes. Cryptography and Communications.

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Journal Article | Epub ahead of print | English
Author
Köse, SeydaISTA; Özbudak, Ferruh
Department
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 Solé 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.
Publishing Year
Date Published
2022-03-09
Journal Title
Cryptography and Communications
Acknowledgement
The authors would like to thank Prof. Dr. Minjia Shi for bringing [13, Conjecture 3.5] to our attention. We would also like to thank the associate editor and anonymous reviewers for their valuable comments and suggestions which improved and clarified the manuscript.
IST-REx-ID

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Köse S, Özbudak F. Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes. Cryptography and Communications. 2022. doi:10.1007/s12095-022-00557-8
Köse, S., & Özbudak, F. (2022). Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes. Cryptography and Communications. Springer Nature. https://doi.org/10.1007/s12095-022-00557-8
Köse, Seyda, and Ferruh Özbudak. “Factorization of Some Polynomials over Finite Local Commutative Rings and Applications to Certain Self-Dual and LCD Codes.” Cryptography and Communications. Springer Nature, 2022. https://doi.org/10.1007/s12095-022-00557-8.
S. Köse and F. Özbudak, “Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes,” Cryptography and Communications. Springer Nature, 2022.
Köse S, Özbudak F. 2022. Factorization of some polynomials over finite local commutative rings and applications to certain self-dual and LCD codes. Cryptography and Communications.
Köse, Seyda, and Ferruh Özbudak. “Factorization of Some Polynomials over Finite Local Commutative Rings and Applications to Certain Self-Dual and LCD Codes.” Cryptography and Communications, Springer Nature, 2022, doi:10.1007/s12095-022-00557-8.

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