A diagonal form for the incidence matrices of t-subsets vs. k-subsets
European Journal of Combinatorics
On the p-Rank of the Adjacency Matrices of Strongly Regular Graphs
Journal of Algebraic Combinatorics: An International Journal
On Modular Standard Modules of Association Schemes
Journal of Algebraic Combinatorics: An International Journal
Representations of finite association schemes
European Journal of Combinatorics
A modular absolute bound condition for primitive association schemes
Journal of Algebraic Combinatorics: An International Journal
Codes associated with triangular graphs and permutation decoding
International Journal of Information and Coding Theory
Codes from lattice and related graphs, and permutation decoding
Discrete Applied Mathematics
Hulls of codes from incidence matrices of connected regular graphs
Designs, Codes and Cryptography
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Let Γ be a distance-regular graph with adjacency matrix A. Let I be the identity matrix and J the all-1 matrix. Let p be a prime. We study the p-rank of the matrices A + bJ − cI for integral b, c and the p-rank of corresponding matrices of graphs cospectral with Γ.Using the minimal polynomial of A and the theory of Smith normal forms we first determine which p-ranks of A follow directly from the spectrum and which, in general, do not. For the p-ranks that are not determined by the spectrum (the so-called relevant p-ranks) of A the actual structure of the graph can play a rôle, which means that these p-ranks can be used to distinguish between cospectral graphs.We study the relevant p-ranks for some classes of distance-regular graphs and try to characterize distance-regular graphs by their spectrum and some relevant p-rank.