  Negacyclic BCH codes are a subclass of neagcyclic codes and are the best
linear codes in many cases. However, there have been very few results on
negacyclic BCH codes. Let $q$ be an odd prime power and $m$ be a positive
integer. The objective of this paper is to study negacyclic BCH codes with
length $\frac{q^m-1}{2}$ and $\frac{q^m+1}{2}$ over the finite field
$\mathbf(q)$ and analyse their parameters. The negacyclic BCH codes presented
in this paper have good parameters in general, and contain many optimal linear
codes. For certain $q$ and $m$, compared with cyclic codes with the same
dimension and length, the negacyclic BCH codes presented in this paper have a
larger minimum distance in some cases.
