Negacyclic BCH codes are an important subclass of negacyclic codes, which have efficient encoding and decoding algorithms, but their parameters are difficult to determine. In this paper, we mainly study two types of negacyclic BCH codes of length $n=\frac{q^{m}-1}{4},\frac{q^{m}+1}{4}$. As byproducts, we investigate the first three largest odd coset leaders modulo $n$. The parameters of two types of negacyclic BCH codes are analysed with small and large dimensions, and the weight distribution of neagcyclic BCH codes of length $n=\frac{q^m-1}{4}$ are determined for designed distance in some ranges.

翻译：负循环BCH码是负循环码的重要子类，具有高效的编码与译码算法，但其参数难以确定。本文主要研究长度为$n=\frac{q^{m}-1}{4},\frac{q^{m}+1}{4}$的两类负循环BCH码。作为副产品，我们探讨了模$n$的前三个最大奇陪集首。分析了两类负循环BCH码在小维数和大维数下的参数，并确定了长度为$n=\frac{q^m-1}{4}$的负循环BCH码在部分设计距离范围内的重量分布。