Maximal Sets of Pairwise Orthogonal Vectors in Finite Fields

http://dx.doi.org/10.4153/CMB-2011-160-x
Canad. Math. Bull. 55(2012), 418-423

  Published:2011-09-15
 Printed: Jun 2012

Given a positive integer $n$, a finite field $\mathbb{F}_q$ of $q$ elements ($q$ odd), and a non-degenerate symmetric bilinear form $B$ on $\mathbb{F}_q^n$, we determine the largest possible cardinality of pairwise $B$-orthogonal subsets $\mathcal{E} \subseteq \mathbb{F}_q^n$, that is, for any two vectors $\mathbf{x}, \mathbf{y} \in \mathcal{E}$, one has $B (\mathbf{x}, \mathbf{y}) = 0$.