三类BCH码及其对偶

SIAM J. Discret. Math. Pub Date : 2022-11-28 DOI:10.48550/arXiv.2211.15350

Yanhui Zhang

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引用次数: 0

摘要

BCH码是一类重要的循环码，在通信和存储系统中有着广泛的应用。然而，BCH码的参数很难确定，已知的病例很少。本文主要研究了三种基于$n=q^{m}-1,\frac{q^{2s}-1}{q+1},\frac{q^{m}-1}{q-1}$的BCH码。一方面，我们准确地给出了$\mathcal C_{(q,n,\delta,1)}$及其双码的参数。另一方面，给出了$\mathcal C_{(q,n,\delta,2)}$是双bch码的充要条件。

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Three classes of BCH codes and their duals

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.

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SIAM J. Discret. Math.

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