Parameters of LCD BCH codes with two lengths

In this paper, we study LCD BCH codes over the finite field GF$(q)$ with two types of lengths $n$, where $n = q^l+1$ and $n = (q^l+1)/(q+1)$. Several classes of LCD BCH codes are given and their parameters are determined or bounded by exploring the cyclotomic cosets modulo $n$. For $n = q^l+1$, we determine the dimensions of the codes with designed distance $δ$, where $q^{\lfloor\frac{l+1}{2}\rfloor}+1 ≤ δ ≤q ^{\lfloor\frac{l+3}{2}\rfloor}+1$. For $n = (q^l+1)/(q+1)$, the dimensions of the codes with designed distance $δ$ are presented, where $2 ≤ δ ≤q ^\frac{l-1}{2}+1$.