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Maximal Sets of Pairwise Orthogonal Vectors in Finite Fields

 Printed: Jun 2012
  • Le Anh Vinh,
    Mathematics Department, Harvard University, Cambridge, MA, 02138, USA
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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 $\mathcal{E} \subseteq \mathbb{F}_q^n$, 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 orthogonal sets, zero-distance sets
MSC Classifications: 05B25 show english descriptions Finite geometries [See also 51D20, 51Exx] 05B25 - Finite geometries [See also 51D20, 51Exx]

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