Binary duadic codes are an interesting subclass of cyclic codes since they have large dimensions and their minimum distances may have a square-root bound. In this paper, we present several families of binary duadic codes of length $2^m-1$ and develop some lower bounds on their minimum distances by using the BCH bound on cyclic codes, which partially solves one case of the open problem proposed in \cite{LLD}. It is shown that the lower bounds on their minimum distances are close to the square root bound. Moreover, the parameters of the dual and extended codes of these binary duadic codes are investigated.

翻译：二元对偶码是循环码中一类有趣的子类，因为它们具有较大的维数且其最小距离可能存在平方根界。本文给出了长度为$2^m-1$的若干族二元对偶码，并利用循环码的BCH界推导了它们最小距离的下界，部分解决了文献\cite{LLD}中提出的一个公开问题。研究表明，这些最小距离的下界接近平方根界。此外，还研究了这些二元对偶码的对偶码和扩展码的参数。