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Explicit expression of the krawtchouk polynomial via a discrete green's function

Title
Explicit expression of the krawtchouk polynomial via a discrete green's function
Authors
Kim G.C.Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2013
Journal Title
Bulletin of the Korean Mathematical Society
ISSN
1015-8634JCR Link
Citation
vol. 50, no. 3, pp. 509 - 527
Indexed
SCIE; SCOPUS; KCI WOS scopus
Abstract
A Krawtchouk polynomial is introduced as the classical Mac- Williams identity, which can be expressed in weight-enumerator-free form of a linear code and its dual code over a Hamming scheme. In this paper we find a new explicit expression for the p-number and the q- number, which are more generalized notions of the Krawtchouk poly- nomial in the P-polynomial schemes by using an extended version of a discrete Green's function. As corollaries, we obtain a new expression of the Krawtchouk polynomial over the Hamming scheme and the Eber- lein polynomial over the Johnson scheme. Furthermore, we find another version of the MacWilliams identity over a Hamming scheme. © 2013 The Korean Mathematical Society.
DOI
10.4134/JKMS.2013.50.3.509
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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