Further results on several classes of optimal ternary cyclic codes with minimum distance four

Qian Liu; Xiaobei Dong; Ximeng Liu; Jian Zou

Paper 2023/888

Further results on several classes of optimal ternary cyclic codes with minimum distance four

Qian Liu

, College of Computer and Data Science, Fuzhou University, Key Laboratory of Information Security of Network Systems, Fuzhou University

Xiaobei Dong, College of Computer and Data Science, Fuzhou University

Ximeng Liu, College of Computer and Data Science, Fuzhou University

Jian Zou, College of Computer and Data Science, Fuzhou University

Abstract

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, by analyzing the solutions of certain equations over $\mathbb{F}_{3^m}$ and using the multivariate method, we present three classes of optimal ternary cyclic codes in the case of $m$ is odd and five classes of optimal ternary cyclic codes with explicit values $e$, respectively. In addition, two classes of optimal ternary cyclic codes $C_{(u, v)}$ are given.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
Keywords: Cyclic code Optimal code Ternary code Sphere packing bound.
Contact author(s): lqmova @ foxmail com
x b dong @ qq com
snbnix @ gmail com
fzuzoujian15 @ 163 com
History: 2023-06-12: approved; 2023-06-09: received; See all versions
Short URL: https://ia.cr/2023/888
License: CC BY

BibTeX

@misc{cryptoeprint:2023/888,
      author = {Qian Liu and Xiaobei Dong and Ximeng Liu and Jian Zou},
      title = {Further results on several classes of optimal ternary cyclic codes with minimum distance four},
      howpublished = {Cryptology ePrint Archive, Paper 2023/888},
      year = {2023},
      note = {\url{https://eprint.iacr.org/2023/888}},
      url = {https://eprint.iacr.org/2023/888}
}