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On cyclotomic schemes over finite near-fields

Authors:	J Bagherian Ilia Ponomarenko A Rahnamai Barghi

Institution:	(1) Institute for Advanced Studies in Basic Sciences (IASBS), P.O. Box 45195-1159, Zanjan, Iran;(2) Petersburg Department of V.A. Steklov Institute of Mathematics, Fontanka 27, St. Petersburg, 191023, Russia

Abstract:	We introduce a concept of cyclotomic association scheme over a finite near-field $\mathbb{K}$ . It is proved that any isomorphism of two such nontrivial schemes is induced by a suitable element of the group AGL(V), where V is the linear space associated with $\mathbb{K}$ . A sufficient condition on a cyclotomic scheme $\mathcal{C}$ that guarantee the inclusion $\mathrm{Aut}(\mathcal{C})\le \mathrm{A} \Gamma \mathrm{L}(1,\mathbb{F}),$ where $\mathbb{F}$ is a finite field with $\|\mathbb{K}\|$ elements, is given. I. Ponomarenko partially supported by RFFI, grants 03-01-00349, NSH-2251.2003.1.

Keywords:	Association scheme Finite near-field Permutation group
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