Recurrent Construction of MacWilliams and Chebyshev Matrices

• Autorzy: Gogin N. , Hirvensalo M.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

orthogonal polynomials; Krawtchouk polynomials; discrete Chebyshev polynomials; MacWilliams transform; MacWilliams matrices; Chebyshev matrices; recursion theory; Krawtchouk coefficients

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2012
• Tom: Vol. 116, nr 1-4
• Strony: 93--110
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Gogin N.

autor

Hirvensalo M.

• Department of Mathematics, University of Turku FI-20014 Turku, Finland and TUCS – Turku Centre for Computer Science,

Bibliografia

• [1] M. Hirvensalo: Studies on Boolean Functions Related to Quantum Computing. Ph.D. thesis, University of Turku (2003).
• [2] F.J. MacWilliams and N.J.A. Sloane: The Theory of Error-Correcting Codes. North-Holland (1977).
• [3] H. Bateman and A. Erdelyi: Higher Transcendental Functions. Vol. 2, McGraw-Hill (1953).
• [4] I.M. Gessel and R. P. Stanley: Algebraic Enumeration. In R. L. Graham, M. Grötschel, L. Lovász (eds.): Handbook of Combinatorics Vol II. Elsevier Science & MIT Press (1995).
• [5] ypreobrazovani_ English variant: N.D. Gogin and A.A. Mylläri: The Fibonacci-Padovan Sequence and MacWilliams Transform Matrices. Programming and Computing Software Vol 33:2, pp. 74-79 (2007).
• [6] A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis. Dover (1975).
• [7] G. Szegö: Orthogonal Polynomials. Providence, Rhode Island: American Mathematical Society, Colloquium Publications, Volume XXIII (1975).