BCH codes are an important class of cyclic codes, and have wide applicantions in communication and storage systems. However, it is difficult to determine the parameters of BCH codes and only a few cases are known. In this paper, we mainly study three classes of BCH codes with $n=q^{m}-1,\frac{q^{2s}-1}{q+1},\frac{q^{m}-1}{q-1}$. On one hand, we accurately give the parameters of $\mathcal C_{(q,n,\delta,1)}$ and its dual codes. On the other hand, we give the sufficient and necessary conditions for $\mathcal C_{(q,n,\delta,2)}$ being dually-BCH codes.
翻译：BCH代码是一个重要的周期代码类别,在通信和储存系统中具有广泛的应用性。 但是,很难确定 BCH代码的参数, 并且只知道少数案例。 在本文中, 我们主要研究三种 BCH 代码, 以 $=q ⁇ m}-1,\ frac{q ⁇ 2s}-1qq+1},\ frac{q{q ⁇ m}-1qq}-1q}1美元。 一方面, 我们准确地给出了$\ mathcal C ⁇ ( q, n,\delta, 1) 及其双重代码的参数。 另一方面, 我们给出了足够和必要的条件, $\ mathc>( q, n,\delta, 2) 美元是双重 BCH 代码 。
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