Dimensions of some LCD BCH codes

Abstract

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 $2\le \delta \le \frac{q^{\lfloor (m+1)/2\rfloor }}{\lambda }+1$, 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.