On Krawtchouk Transforms
In: Intelligent Computer Mathematics ; 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010 ; https://hal.archives-ouvertes.fr/hal-00537884 ; 10th International Conference, 2010
Konferenz
Zugriff:
International audience ; Krawtchouk polynomials appear in a variety of contexts, most notably as orthogonal polynomials and in coding theory via the Krawtchouk transform. We present an operator calculus formulation of the Krawtchouk transform that is suitable for computer implementation. A positivity result for the Krawtchouk transform is shown. Then our approach is compared with the use of the Krawtchouk transform in coding theory where it appears in MacWilliams' and Delsarte's theorems on weight enumerators. We conclude with a construction of Krawtchouk polynomials in an arbitrary finite number of variables, orthogonal with respect to the multinomial distribution.
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On Krawtchouk Transforms
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Autor/in / Beteiligte Person: | Feinsilver, Philip ; Schott, René ; Southern Illinois University Carbondale (SIU) ; Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA) ; Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria) ; Institut Élie Cartan de Nancy (IECN) ; Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria) ; Autexier, Serge ; Calmet, Jacques ; Delahaye, David ; Patrick D.F. Ion and Laurence Rideau |
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Zeitschrift: | Intelligent Computer Mathematics ; 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010 ; https://hal.archives-ouvertes.fr/hal-00537884 ; 10th International Conference, 2010 |
Veröffentlichung: | HAL CCSD ; Springer, 2010 |
Medientyp: | Konferenz |
DOI: | 10.1007/978-3-642-14128-7_7 |
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