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

Koese S., ÖZBUDAK F.

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, cilt.14, sa.4, ss.933-948, 2022 (SCI-Expanded) identifier identifier

  • 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.