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. 14(4), 933–948.
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Journal Article
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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.
Keywords
Publishing Year
Date Published
2022-07-01
Journal Title
Cryptography and Communications
Publisher
Springer Nature
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.
Volume
14
Issue
4
Page
933-948
ISSN
eISSN
IST-REx-ID
Cite this
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;14(4):933-948. 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, vol. 14, no. 4. Springer Nature, pp. 933–948, 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. 14(4), 933–948.
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, vol. 14, no. 4, Springer Nature, 2022, pp. 933–48, doi:10.1007/s12095-022-00557-8.
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