The weight distributions of some cyclic codes with three or four nonzeros over F3

TL;DR

This paper determines the weight distributions of specific cyclic codes with three or four nonzeros over F3, expanding understanding beyond the previously known cases with fewer nonzeros.

Contribution

It provides the first explicit weight distribution results for cyclic codes with three or four nonzeros, which were previously unknown.

Findings

Weight distributions for two classes of cyclic codes with three nonzeros

Weight distributions for two classes of cyclic codes with four nonzeros

Enhanced understanding of code properties for communication systems

Abstract

Because of efficient encoding and decoding algorithms, cyclic codes are an important family of linear block codes, and have applications in communica- tion and storage systems. However, their weight distributions are known only for a few cases mainly on the codes with one or two nonzeros. In this paper, the weight distributions of two classes of cyclic codes with three or four nonzeros are determined.