Title: Several classes of optimal ternary cyclic codes,
Abstract: Cyclic codes have efficient encoding and decoding algorithms over finite
fields, so that they have practical applications in communication systems,
consumer electronics and data storage systems. The objective of this paper is
to give eight new classes of optimal ternary cyclic codes with parameters
$[3^m-1,3^m-1-2m,4]$, according to a result on the non-existence of solutions
to a certain equation over $F_{3^m}$. It is worth noticing that some recent
conclusions on such optimal ternary cyclic codes are some special cases of our
work. More importantly, three of the nine open problems proposed by Ding and
Helleseth in [8] are solved completely. In addition, another one among the nine
open problems is also promoted.