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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 
$\varepsilon \,\subseteq \,\mathbb{F}_{q}^{n}$, that is, for any two vectors 
$x,\,y\,\in \,\varepsilon $, one has 
$B(x,\,y)\,=\,0$.
