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.

翻译：BCH代码因其有效的编码和解码算法而是一个有趣的周期代码类别,在许多情况下,BCH代码是最好的线性代码,然而,BCH代码的尺寸和最小距离很少解决,到目前为止,在超过$gf(q)美元、长度为$q ⁇ m+1美元的BCH代码方面,结果很少,特别是当$q是主要功率,$m+1美元是偶数时。本文的目的是研究这种类型的BCH代码相对于有限的领域,并分析其参数。本文中介绍的BCH代码一般具有良好的参数,包含许多最佳线性代码。