On the Number of ℤp-Double Cyclic Codes and Quasi Cyclic Codes

Abualrub T., Aydoğdu İ., Yıldız E., Khashyarmanesh K.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.23, pp.1-12, 2024 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 23
  • Publication Date: 2024
  • Doi Number: 10.1142/s0219498824502153
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1-12
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we study the class of Zp-double cyclic codes of length n = r + s. We give a closed formula for the number of Zp-double cyclic codes of length n = r+s, for any integers r and s that are relatively prime to p. Moreover, we give a closed formula for the number of quasi-cyclic (QC) codes of length n = 2s and index 2. We also provide formulas for the number of separable and non-separable Zp-double cyclic codes of length n. In order to illustrate the results, we calculate the number of some codes with different r and s. Moreover, we list optimal parameter Z2-double cyclic codes for specific values of r and s.