Recurrent Construction of MacWilliams and Chebyshev Matrices

Issue title: Words, Graphs, Automata, and Languages; Special Issue Honoring the 60th Birthday of Professor Tero Harju

Article type: Research Article

Authors: Gogin, Nikita | Hirvensalo, Mika

Affiliations: ngiri@lsi.ru | Department of Mathematics, University of Turku, FI-20014 Turku, Finland and TUCS – Turku Centre for Computer Science, mikhirve@utu.fi

Note: [] Address for correspondence: Department of Matematics, University of Turku, FI-20014 Turku, Finland This work has been partially supported by the Academy of Finland under grant 208797.

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.

Keywords: Orthogonal polynomials, Krawtchouk polynomials, discrete Chebyshev polynomials, MacWilliams transform, MacWilliams matrices, Chebyshev matrices, Recursion, Krawtchouk coefficients

DOI: 10.3233/FI-2012-671

Journal: Fundamenta Informaticae, vol. 116, no. 1-4, pp. 93-110, 2012