Parameters of several families of binary duadic codes and their related codes

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 2m-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^m-1$$\end{document} 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 Liu et al (Finite Field Appl 91:102270, 2023). 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.