Linear codes with complementary duals (LCD codes) have attracted a lot of interest in recent years due to their applications in data storage, protections against fault injection attacks and implementations against side-channel attacks. The objective of this paper is to investigate some ternary LCD cyclic codes with length \(\varvec{n} \varvec{=} \frac{\varvec{3}^{\varvec{2m}} \varvec{-1}}{\varvec{4}}\) . The dimension of LCD BCH codes \(\varvec{\mathcal {C}}_{\varvec{(3,n,2\delta ,-\delta +1)}}\) is determined, where \(\varvec{2}\varvec{\le \delta \le } \varvec{3}^{\varvec{m+1}}\) . Moreover, we calculate the minimum distance of some of these LCD BCH codes with specific designed distance. By calculating the first three largest absolute coset leaders modulo \(\varvec{n}\) , we construct several classes of ternary LCD cyclic codes. The weight distribution of some of them is given.
