Abstract
Cyclic code is an interesting topic in coding theory and communication
systems. In this paper, two families of optimal ternary cyclic codes
with parameters $[3^m-1,3^m-2m-1,4]$ are presented. The
first family of cyclic codes with two zeros $\pi$ and
$\pi^v$ is constructed by using multivariate method.
The second family of cyclic codes with two zeros
$\pi^2$ and $\pi^v$ is obtained
by analyzing irreducible factors of certain polynomials with finite
degrees over the finite field
$\mathbb{F}_{3^m}$, where
$\pi$ is a generator of
$\mathbb{F}_{3^m}^*$.