Infinite families of 2-designs from two classes of binary cyclic codes with three nonzeros

<p style='text-indent:20px;'>Combinatorial <inline-formula><tex-math id="M1">\begin{document}$ t $\end{document}</tex-math></inline-formula>-designs have been an interesting topic in combinatorics for decades. It is a basic fact that the codewords of fixed weight code may hold id="M2">\begin{document}$ $\end{document}</tex-math></inline-formula>-design. Till now only small amount work on constructing id="M3">\begin{document}$ from codes has done. In this paper, we determine distributions two classes cyclic codes: one related to triple-error correcting binary BCH codes, and other with parameters satisfying generalized Kasami case, respectively. We then obtain infinite families id="M4">\begin{document}$ 2 these by proving they are both affine-invariant explicitly their parameters. particular, derived dual five id="M5">\begin{document}$ 3 when id="M6">\begin{document}$ m = 4 $\end{document}</tex-math></inline-formula>.</p>