Characterization of p-ary functions in terms of association schemes and its applications.

We obtain an explicit criterion for p -ary functions to produce association schemes in terms of their Walsh spectrum. Employing this characterization, we explicitly find a correlation between p -ary bent functions and association schemes; to be more exact, we prove that a p -ary bent function induces a p -class association scheme if and only if the function is weakly regular. As applications of our main criterion, we construct many infinite families of few-class association schemes arising from p -ary functions. Furthermore, we present four classes of p -ary two-weight linear codes, which are constructed from the association schemes produced in this paper. [ABSTRACT FROM AUTHOR]