Non-trivial $t$-intersecting families for the distance-regular graphs of bilinear forms

Abstract

Let V be an (n + ℓ)-dimensional vector space over a finite field, and W a fixed ℓ-In this paper, we describe the structure of non-trivial t-intersecting families of V n,0 with large size. In particular, we show the structure of the non-trivial t-intersecting families with maximum size, which extends the Hilton-Milner Theorem for V n,0 .