  BCH codes are an interesting class of cyclic codes due to their efficient
encoding and decoding algorithms. In many cases, BCH codes are the best linear
codes. However, the dimension and minimum distance of BCH codes have been
seldom solved. Until now, there have been few results on BCH codes over
$\gf(q)$ with length $q^m+1$, especially when $q$ is a prime power and $m$ is
even. The objective of this paper is to study BCH codes of this type over
finite fields and analyse their parameters. The BCH codes presented in this
paper have good parameters in general, and contain many optimal linear codes.
