A construction of association schemes from vectors in orthogonal spaces of odd characteristic

Abstract

Let double-struck F sign_q be a finite field of odd characteristic, n = 2v + δ, v ≥ 2, δ = 0, 1, or 2, and 1 ≤ t < v. Using the isotropic vectors whose (v + l)-th coordinates are fixed in the (2v + δ)-dimensional orthogonal space over double-struck F sign_q, where 1 ≤ l ≤ t, we construct an association scheme with q associate classes. The parameters are computed. Finally we obtain an authentication code with perfect secrecy from this association scheme.