On the number of Z(2)Z(4) and Z(p)Z(p2)-additive cyclic codes

YILDIZ E., Abualrub T., AYDOĞDU İ.

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, cilt.34, sa.1, ss.81-97, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s00200-020-00474-4
  • Dergi Adı: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.81-97
  • Anahtar Kelimeler: Z(2)Z(4)-additive cyclic codes, Z(p)Z(p2)-additive cyclic codes, counting, separable, non-separable codes
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we give the exact number of Z(2)Z(4)-additive cyclic codes of length n = r + s, for any positive integer r and any positive odd integer s. We will provide a formula for the the number of separable Z(2)Z(4)-additive cyclic codes of length n and then a formula for the number of non-separable Z(2)Z(4)-additive cyclic codes of length n. Then, we have generalized our approach to give the exact number of Z(p)Z(p2)-additive cyclic codes of length n = r + s, for any prime p, any positive integer r and any positive integer s where gcd (p, s) = 1. Moreover, we will provide examples of the number of these codes with different lengths n = r + s.