Two families of optimal ternary cyclic codes with minimal distance four

Abstract

In this paper, the two families of optimal ternary cyclic codes with parameters of [3m−1,3m−1−2m,4] are presented. Some conclusions proposed by Wang and Wu in 2016 are analyzed and refined, and the remaining problem in it is solved. In addition, a conjecture proposed by Ding and Helleseth in 2013 about a class of optimal ternary cyclic codes C(1,e) in which e=(3m−1−1)/2+3h+1 with parameters [3m−1,3m−2m−1,4] is analyzed, where 0≤h≤m−1.