In this paper, we investigate the first few largest coset leaders modulo $\frac{q^m+1}{\lambda}$ where $\lambda\mid q+1$ and $q$ is an odd prime power, and give the dimensions of some LCD BCH codes of length $\frac{q^m+1}{\lambda}$ with large designed distances.We also determine the dimensions of some LCD BCH codes of length $n=\frac{(q^m+1)}{\lambda}$ with designed distances $2\leq \delta \leq \frac{ q^{\lfloor(m+1)/2\rfloor}}{\lambda}+1$, where $ \lambda\mid q+1$ and $1<\lambda<q+1$. The LCD BCH codes presented in this paper have a sharper lower bound on the minimum distance than the BCH bound.

翻译：本文研究模$\frac{q^m+1}{\lambda}$的前几个最大陪集首（其中$\lambda\mid q+1$且$q$为奇素数幂），并给出具有大设计距离的某些长度为$\frac{q^m+1}{\lambda}$的LCD BCH码的维数。我们还确定了设计距离$2\leq \delta \leq \frac{ q^{\lfloor(m+1)/2\rfloor}}{\lambda}+1$（其中$\lambda\mid q+1$且$1<\lambda<q+1$）的长度$n=\frac{(q^m+1)}{\lambda}$的某些LCD BCH码的维数。本文给出的LCD BCH码在最小距离上比BCH界具有更优的下界。