On the Assmus--Mattson type theorem for Type I and even formally self-dual codes

Abstract

In the present paper, we give the Assmus--Mattson type theorem for near-extremal Type I and even formally self-dual codes. We show the existence of $1$-designs or $2$-designs for these codes. As a corollary, we prove the uniqueness of a self-orthogonal $2$-$(16,6,8)$ design.