Several new classes of optimal ternary cyclic codes with two or three zeros

Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let $\alpha $ be a generator of $\mathbb{F}{3^m}*$, where $m$ is a positive integer. Denote by $\mathcal{C}{(i1,i2,\cdots, it)}$ the cyclic code with generator polynomial $m{\alpha^{{i1}}(x)m{\alpha{i_2}}(x)\cdots} m{\alpha^{it}}(x)$, where ${{m}{\alpha^{i}}}(x)$ is the minimal polynomial of ${{\alpha }^{i}}$ over ${{\mathbb{F}}{3}}$. In this paper, by analyzing the solutions of certain equations over finite fields, we present four classes of optimal ternary cyclic codes $\mathcal{C}{(0,1,e)}$ and $\mathcal{C}{(1,e,s)}$ with parameters $[3^{m-1,3m-\frac{3m}{2}-2,4]$,} where $s=\frac{3^m-1}{2}$. In addition, by determining the solutions of certain equations and analyzing the irreducible factors of certain polynomials over $\mathbb{F}{3^m}$, we present four classes of optimal ternary cyclic codes $\mathcal{C}{(2,e)}$ and $\mathcal{C}_{(1,e)}$ with parameters $[3^{m-1,3m-2m-1,4]$.} We show that our new optimal cyclic codes are inequivalent to the known ones.