Five Families of Three-Weight Ternary Cyclic Codes and Their Duals

TL;DR

This paper introduces five new families of three-weight ternary cyclic codes with duals having two zeros, providing their weight distributions and identifying two optimal dual families, advancing coding theory applications.

Contribution

The paper presents five new families of three-weight ternary cyclic codes with explicitly determined weight distributions and identifies two optimal dual code families.

Findings

Weight distributions of five cyclic code families are determined.

Duals of two families are proven to be optimal.

Codes have applications in efficient data encoding.

Abstract

As a subclass of linear codes, cyclic codes have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, five families of three-weight ternary cyclic codes whose duals have two zeros are presented. The weight distributions of the five families of cyclic codes are settled. The duals of two families of the cyclic codes are optimal.