论文标题
三类BCH代码及其双重
Three classes of BCH codes and their duals
论文作者
论文摘要
BCH代码是一类重要类别的循环代码，并且在通信和存储系统中具有广泛的申请。但是，很难确定BCH代码的参数，并且仅知道少数情况。在本文中，我们主要研究了三类的BCH代码，其中$ n = q^{m} -1，\ frac {q^{2S} -1} -1} {q+1}，\ frac {q^{m} -1} -1} {q-1} {q-1} $。一方面，我们准确地给出了$ \ Mathcal c _ {（q，n，δ，1）} $的参数及其双重代码。另一方面，我们为$ \ Mathcal C _ {（q，n，δ，2）} $提供了足够和必要的条件。
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 $\mathcal C_{(q,n,δ,1)}$ and its dual codes. On the other hand, we give the sufficient and necessary conditions for $\mathcal C_{(q,n,δ,2)}$ being dually-BCH codes.
