Some results on the antiprimitive BCH codes

BCH codes are an important class of cyclic codes due to their efficient encoding and decoding algorithms, antiprimitive BCH codes have taken a lot of attention in recent years. In this paper, we mainly study a class of BCH codes of length $n=\frac{q^{m}+1}{\lambda}$, where $\lambda\mid (q+1)$ is an integer. We give several classes of BCH codes with good parameters in this paper, containing many optimal linear codes. We also present the first few largest coset leaders modulo $n$, so two conjectures about BCH codes are partially solved.