Infinite families of $ t $-designs and strongly regular graphs from punctured codes

Abstract

<p style='text-indent:20px;'>The puncturing technique is sometimes efficient in constructing projective codes from original codes which are not projective. In this paper, several families of projective linear codes punctured from reducible cyclic codes, special linear codes or irreducible cyclic codes are investigated. The parameters and weight enumerators of the punctured codes and their duals are explicitly determined. Some of the codes are optimal and some of the codes are self-orthogonal which can be used to construct quantum codes. Several infinite families of combinatorial <inline-formula><tex-math id="M2">\begin{document}$ 2 $\end{document}</tex-math></inline-formula>-designs and <inline-formula><tex-math id="M3">\begin{document}$ 3 $\end{document}</tex-math></inline-formula>-designs including some families of Steiner systems are constructed from the punctured codes and their duals. Besides, infinite families of strongly regular graphs are also derived from some families of two-weight projective codes.</p>