Negacyclic BCH codes are an important subclass of negacyclic codes and have good parameters. Inspired by the recent work on cyclic codes published in Wu et al. (Finite Fields Appl 60:101581, 2019), the objective of this paper is to investigate the parameters of the narrow-sense negacyclic BCH codes of length \(n=\frac{q^{2m}-1}{q+1}\) over \({\textrm{GF}}(q)\), where q is an odd prime power. For \(2\le \delta \le \left\lfloor \frac{q^{m+1}-q}{q+1} \right\rfloor +2\), the dimension of the narrow-sense negacyclic BCH codes of length n with designed distance \(\delta \) is determined. For \(2\le \delta \le \frac{q^{2m-1}+1}{q+1}\), a lower bound on the minimum distance of the dual codes of the narrow-sense negacyclic BCH codes of length n with designed distance \(\delta \) is presented. Compared with cyclic codes, we obtain some negacyclic BCH codes with better parameters.

负循环BCH码是负循环码的重要子类，具有良好的参数。受到 Wu 等人最近发表的循环码工作的启发。(Finite Fields Appl 60:101581, 2019)，本文的目的是研究长度为\(n=\frac{q^{2m}-1}{q+1)的狭义负循环 BCH 码的参数}\)超过\({\textrm{GF}}(q)\)，其中q是奇素数幂。对于\(2\le \delta \le \left\lfloor \frac{q^{m+1}-q}{q+1} \right\rfloor +2\) ，狭义负循环 BCH 的维数确定长度为n且设计距离\(\delta \)的代码。对于\(2\le \delta \le \frac{q^{2m-1}+1}{q+1}\)，狭义负循环 BCH 码的对偶码的最小距离的下界给出了长度为n和设计距离\(\delta \)的。与循环码相比，我们得到了一些参数更好的负循环BCH码。