Generalizing Krawtchouk polynomials using Hadamard matrices (Q469931)

Summary: We investigate polynomials, called \(m\)-polynomials, whose generator polynomial has coefficients that can be arranged in a square matrix; in particular, the case where this matrix is a Hadamard matrix is considered. Orthogonality relations and recurrence relations are established, and coefficients for the expansion of any polynomial in terms of \(m\)-polynomials are obtained. We conclude this paper by an implementation of \(m\)-polynomials and some of the results obtained for them in Mathematica.