As a generalization of attenuated spaces, the concept of singular linear spaces was introduced
in [K. Wang, J. Guo, F. Li, Association schemes based on attenuated spaces, European J. …

The subspaces of a given dimension in an attenuated space form the points of an association
scheme. If the dimension is maximal, it is the bilinear forms graph, which has been …

Meemark and Prinyasart [10] proved by combinatorial method that the symplectic graph [Formula:
see text] modulo p n is strongly regular when ν=1, and [Formula: see text] is arc …

A resolving set of a graph is a set of vertices with the property that the list of distances from
any vertex to those in the set uniquely identifies that vertex. In this paper, we construct a …

Let AG(n, F q ) be the n-dimensional affine space over F q , where F q is a finite field with q
elements. Denote by Γ (m) the graph induced by m-flats of AG(n, F q ). For any two adjacent …

Suppose F q n+l denotes the (n+l)-dimensional vector space over a finite field F q and GL n+l,n
(F q ) denotes the corresponding singular general linear group. All the subspaces of type …

Let d , k , n be integers with 1 ≤ d < k ≤ n − d . In Kantor (1972), Kantor proved that the
incidence matrix of d -dimensional subspaces versus k -dimensional subspaces of an n -…

Let R denote the Galois ring of characteristic p s and cardinality p s h . In this paper, we
determine the Smith normal forms of matrices over R, compute the number of the orbits of m × n …

Dual polar schemes are well-known association schemes [1, 2]. Applying the matrix method,
Wan et al.[5] computed all parameters of dual polar schemes; Wang et al.[4, 8, 9] …

Let F q 2ν be the 2ν-dimensional symplectic space over a finite field F q . For 0≤s≤ν−1 and
ν≥2, let W 0 be a fixed subspace of type (ν+s,s) in F q 2ν , and let X be the set of the 1-…