A Class of New Optimal Ternary Cyclic Codes over F<sub>3<sup><i>m</i></sup></sub> with Minimum Distance 4

Abstract

As a branch of applied mathematics, coding theory plays an important role. Among them, cyclic codes have attracted much attention because of their good algebraic structure and easy analysis performance. In this paper, we will study one class of cyclic codes over 3  . Given the length and dimension, weshow that it is optimal by proving its minimum distance is equal to 4, according to the Sphere Packing bound.