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Maximal Sets of Pairwise Orthogonal Vectors in Finite Fields

Published online by Cambridge University Press:  20 November 2018

Le Anh Vinh
Le Anh Vinh*
Affiliation:
Mathematics Department, Harvard University, Cambridge, MA, 02138, USAe-mail: vinh@math.harvard.edu
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Abstract

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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 $B(x,\,y)\,=\,0$.

Keywords

05B25orthogonal setszero-distance sets
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 2 , 01 June 2012 , pp. 418 - 423
Copyright
Copyright © Canadian Mathematical Society 2012

References

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