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

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 XPtXσP + Y for all XX n , where PGL n (F q ), σ is an automorphism of F q , and YX n .

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Correspondence to Changli Ma.

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2000 Mathematics Subject Classification: 05E30

Supported by the National Natural Science Foundation of China (10271039), Hobei Natural Science Foundation (102132) and Hebei Education Committee.

Communicated by Mulan Liu

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Ma, C., Wang, Y. Automorphisms of Association Schemes of Quadratic Forms over a Finite Field of Characteristic Two. Algebra Colloq. 10, 63–74 (2003). https://doi.org/10.1007/s100110300008

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Keywords:

  • quadratic form
  • association scheme
  • automorphism