The weight distributions of a class of cyclic codes III

TL;DR

This paper determines the weight distribution of a specific class of cyclic codes by evaluating character sums over finite fields using Jacobi sums, extending previous results in the area.

Contribution

It solves a new special case of weight distribution for cyclic codes with two zeros, employing character sum techniques with Jacobi sums.

Findings

Derived explicit weight distribution for the new class of cyclic codes.

Extended the methodology for evaluating character sums in coding theory.

Provided a complete solution for the specific case studied.

Abstract

Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we solve one more special case. The problem of finding the weight distribution is transformed into a problem of evaluating certain character sums over finite fields, which in turn can be solved by using the Jacobi sums directly.