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, vol.34, no.1, pp.81-97, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1007/s00200-020-00474-4
  • Journal Name: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Page Numbers: pp.81-97
  • Keywords: Z(2)Z(4)-additive cyclic codes, Z(p)Z(p2)-additive cyclic codes, counting, separable, non-separable codes
  • Yıldız Technical University Affiliated: Yes

Abstract

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.