Affine orthogonal spaces over finite fields and its applications
Wang Zhao-fei · 2005
Let Fq be a finite field with q elements where q is a power of an odd prime. In this paper,the concepts of affine orthogonal spaces AOG(2ν+δ,Fq) and affine orthogonal group AO2ν+δ,△(Fq)over Fq are given,the transitivity of AO2ν+δ,△(Fq)on AOG(2ν+δ,Fq)is discussed,and some Anzahl theorems in AOG(2ν+δ,Fq) are obtained using actions of AO2ν+δ,△(Fq)on AOG(2ν+δ,Fq). Moreover,we construct an authentication code in view of affine orthogonal spaces.