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, cilt.14, sa.4, ss.933-948, 2022 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14 Sayı: 4
- Basım Tarihi: 2022
- Doi Numarası: 10.1007/s12095-022-00557-8
- Dergi Adı: CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
- Sayfa Sayıları: ss.933-948
- Anahtar Kelimeler: Polynomial factorization, Finite local commutative ring, Self-dual codes, LCD codes, Quasi twisted codes, QUASI-TWISTED CODES, SIDE-CHANNEL
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
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.