The weight distributions of two classes of p ary cyclic codes with few weights

TL;DR

This paper determines the weight distributions of two classes of p-ary cyclic codes with few weights, revealing they have at most five nonzero weights, which is valuable for coding theory applications.

Contribution

The paper provides a complete characterization of the weight distributions for two classes of p-ary cyclic codes with few weights, expanding understanding of their structure.

Findings

Both codes have at most five nonzero weights.

Complete weight distribution formulas are derived.

Results enhance the design of efficient coding schemes.

Abstract

Cyclic codes have attracted a lot of research interest for decades as they have efficient encoding and decoding algorithms. In this paper, for an odd prime $p$, the weight distributions of two classes of $p$-ary cyclic codes are completely determined. We show that both codes have at most five nonzero weights.