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Using covering numbers we prove that a standard real integral table algebra (A, B) with |B| ≥ 6 has a P-polynomial structure with respect to every b = 1 in B if and only if 2|B| − 1 is prime and (A, B) is exactly isomorphic to the Bose-Mesner algebra of the association scheme of the ordinary (2|B| − 1)-gon. Then we present an example showing that this(More)
Hanaki [A. Hanaki, Representations of association schemes and their factor schemes, Graphs Combin. 19 (2003) 195–201; A. Hanaki, Characters of association schemes and normal closed subsets, Graphs Combin. 19 (2003) 363–369] generalized many properties of characters of finite groups to characters of association schemes. In this paper we show that many of(More)
Let G be a finite abelian group acting faithfully on a finite set X. As a natural generalization of the perfect nonlinearity of Boolean functions, the G-bentness and G-perfect nonlinearity of functions on X are studied by Poinsot et al. [6, 7] via Fourier transforms of functions on G. In this paper we introduce the so-called G-dual set X of X, which plays(More)