Abstract
Known results on orthogonal systems and permutation polynomials vectors over finite fields are extended to modular algebras of the form Lν = K[X]/(p(X)ν ), where K is a finite field, p(X) ∈ K[X] is an irreducible polynomial, ν = 1, 2, . . ., and to the algebra of formal power series L[[Z]], where L1 = K[X]/(p(X)) = L.
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