Recurrent Construction of MacWilliams and Chebyshev Matrices

Abstract

We give two recursive expressions for both MacWilliams and Chebyshev matrices. The expressions give rise to simple recursive algorithms for constructing the matrices. In order to derive the second recursion for the Chebyshev matrices we find out the Krawtchouk coefficients of the discrete Chebyshev polynomials, a task interesting on its own.