$t$-designs obtained from two shells and exceptional examples of them

Madoka Awada

Published 2023-10-22Version 1

In this paper, we construct $3$-designs using extended quadratic residue codes over $\mathbb {F}_q$ and their dual codes. We give as a corollary $3$-designs that do not follow from the transitivity argument and the Assmus--Mattson Theorem.