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 ↦ PtXσP + Y for all X ∈ X n , where P ∈ GL n (F q ), σ is an automorphism of F q , and Y ∈ X n .
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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
- quadratic form
- association scheme