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Automorphisms of Association Schemes of Quadratic Forms over a Finite Field of Characteristic Two

Automorphisms of Association Schemes of Quadratic Forms over a Finite Field of Characteristic Two Let X n denote the set of quadratic forms in n variables over a finite field F q of characteristic 2, and X n the association scheme on X n by defining the relations with respect to the type of quadratic forms. We prove that every automorphism of X n is of the form X ↦ P t X σ P + Y for all X ∈ X n , where P ∈ GL n (F q ), σ is an automorphism of F q , and Y ∈ X n . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algebra Colloquium Springer Journals

Automorphisms of Association Schemes of Quadratic Forms over a Finite Field of Characteristic Two

Ma, Changli; Wang, Yangxian
Algebra Colloquium , Volume 10 (1) – Jan 1, 2003
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Publisher
Springer Journals
Copyright
Copyright © 2003 by AMSS CAS
Subject
Mathematics; Algebra; Algebraic Geometry
ISSN
1005-3867
eISSN
0219-1733
DOI
10.1007/s100110300008
Publisher site
See Article on Publisher Site

Abstract

Let X n denote the set of quadratic forms in n variables over a finite field F q of characteristic 2, and X n the association scheme on X n by defining the relations with respect to the type of quadratic forms. We prove that every automorphism of X n is of the form X ↦ P t X σ P + Y for all X ∈ X n , where P ∈ GL n (F q ), σ is an automorphism of F q , and Y ∈ X n .

Journal

Algebra Colloquium – Springer Journals

Published: Jan 1, 2003

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