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.

翻译：BCH码因其高效的编码与译码算法而成为一类重要的循环码，近年来反本原BCH码受到了广泛关注。本文主要研究长度为$n=\frac{q^{m}+1}{\lambda}$的一类BCH码，其中$\lambda\mid (q+1)$为整数。我们给出了若干类具有良好参数的BCH码，包含许多最优线性码。此外，我们还给出了模$n$的前几个最大陪集首，从而部分解决了关于BCH码的两个猜想。