BCH codes are an important class of cyclic codes with wide applications in communication and storage systems. However, compared to primitive LCD BCH codes, LCD properties of BCH codes of length \(\varvec{n=\frac{q^m+1}{r}}\) , \(\varvec{r \nmid (q+1)}\) are seldom studied. In this paper, we investigate the parameters of LCD BCH codes with length \(\varvec{\frac{2^m+1}{5}, \frac{2^m+1}{9}}\) and \(\varvec{\frac{3^m+1}{5}}.\) A new method is proposed to calculate the coset leaders modulo \(\varvec{n}\) , and the dimensions of LCD BCH codes \(\varvec{\mathcal {C}_{(q,n,\delta ,b)}}\) with some given designed distances are determined. Furthermore, we compute the Bose distance of \(\varvec{\mathcal {C}_{(q,n,\delta ,0)}}\) . These results may be helpful to construct other families of LCD BCH codes. Some LCD BCH codes of length \(\varvec{n=\frac{q^m+1}{r}}\) with good minimum weights are constructed.
