Almost orthogonal subsets of vector spaces over finite fields

Abstract

We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In particular, we obtain sharp finite field variants of a theorem of Rosenfeld and an almost version of a theorem of Berlekamp.

26 pages. Minor changes compared to v1

Cited by in corpus (1)

• On the maximum size of ultrametric orthogonal sets over discrete valued fields