Canadian Mathematical Society www.cms.math.ca
Abstract view

# Maximal Sets of Pairwise Orthogonal Vectors in Finite Fields

Published:2011-09-15
Printed: Jun 2012
• Le Anh Vinh,
Mathematics Department, Harvard University, Cambridge, MA, 02138, USA
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
 Format: LaTeX MathJax PDF

## Abstract

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 $B (\mathbf{x}, \mathbf{y}) = 0$.
 Keywords: orthogonal sets, zero-distance sets
 MSC Classifications: 05B25 - Finite geometries [See also 51D20, 51Exx]

© Canadian Mathematical Society, 2013 : http://www.cms.math.ca/