Some constacyclic BCH codes with good parameters

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 \(\lambda \) $\lambda$ -constacyclic BCH codes of length \(q^{m}+1\) $q^m+1$ , where q is a prime power and \(\textrm{ord}(\lambda )\mid q-1\) $\text{ord}(\lambda )\mid q-1$ . 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.