Linear recurring sequences and weight distributions of some cyclic codes

GÜDAY E., ŞAHİN M.

Applicable Algebra in Engineering, Communications and Computing, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s00200-025-00697-3
  • Dergi Adı: Applicable Algebra in Engineering, Communications and Computing
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: Cyclic codes, Fibonacci-like conditional sequences, Linear recurring sequences, Strongly regular graphs
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

In this paper, a family of 2r-dimensional cyclic codes is considered. In some cases, the weight distribution of these codes is determined. For this family of cyclic codes, the upper and lower bounds on the number of non-zero weights that the codes can have are obtained. In addition, it is proved in Shi et al. (Chin J Electron 28(6):1127–113, 2019) that any 2-dimensional cyclic code has at most two non-zero weights, and an open problem is proposed to extend this result to higher-dimensional cyclic codes. This paper also partially solves the open problem. As an application, we construct two families of strongly regular graphs employing 2-weight projective codes and calculate their parameters, eigenvalues, and multiplicities. One of them has the parameters of the Lattice graphs, and the other family has the parameters of the Latin Square graphs.