A class of cyclic codes whose dual have five zeros

TL;DR

This paper introduces a new family of cyclic codes over finite fields with duals having five zeros and determines their weight distributions, advancing understanding of their algebraic and combinatorial properties.

Contribution

It presents a novel class of cyclic codes with specific dual zero properties and explicitly calculates their weight distributions, which was previously unexplored.

Findings

Identified a new family of cyclic codes with five zeros in their duals.

Derived explicit weight distributions for these codes.

Enhanced understanding of the algebraic structure of cyclic codes.

Abstract

In this paper, a family of cyclic codes over $\mathbb{F}_{p}$ whose duals have five zeros is presented, where $p$ is an odd prime. Furthermore, the weight distributions of these cyclic codes are determined.