BCH codes as a subclass of constacyclic BCH codes have been widely studied, while the results on the parameters of BCH codes over finite fields are still very limited. In this paper, we investigate some q-ary BCH codes and \(\lambda \)-constacyclic BCH codes of length \(q^{m}+1\), where q is a prime power and \(\textrm{ord}(\lambda )\mid q-1\). We determine the dimensions of these codes with some large designed distances, and give good lower bounds on the minimum distance. The code examples presented in this paper indicate that these codes contain many distance-optimal codes and codes with best known parameters.

BCH码作为常循环BCH码的一个子类已经得到了广泛的研究，但关于有限域上BCH码的参数的结果仍然非常有限。在本文中，我们研究了一些 q 元 BCH 码和长度为 \(q^{m}+1\) 的 \(\lambda \)-常循环 BCH 码，其中 q 是素数幂，\(\textrm{ord }(\lambda )\mid q-1\)。我们用一些大的设计距离来确定这些代码的尺寸，并给出最小距离的良好下限。本文提供的代码示例表明这些代码包含许多距离最优代码和具有最佳已知参数的代码。