Table of Contents
ISRN Applied Mathematics
Volume 2014 (2014), Article ID 498135, 8 pages
http://dx.doi.org/10.1155/2014/498135
Research Article

Generalizing Krawtchouk Polynomials Using Hadamard Matrices

1Department of Computer Science, Mathematics and Physics, Faculty of Science and Technology, The University of the West Indies, Cave Hill, St. Michael, Barbados
2The University of Trinidad and Tobago, O'Meara Campus, Arima, Trinidad and Tobago

Received 15 November 2013; Accepted 22 December 2013; Published 4 March 2014

Academic Editors: F. Ding and X. Liu

Copyright © 2014 Peter S. Chami et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.