EXPLICIT EXPRESSION OF THE KRAWTCHOUK POLYNOMIAL VIA A DISCRETE GREEN'S FUNCTION

Title & Authors
EXPLICIT EXPRESSION OF THE KRAWTCHOUK POLYNOMIAL VIA A DISCRETE GREEN'S FUNCTION
Kim, Gil Chun; Lee, Yoonjin;

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 $\small{p}$-number and the $\small{q}$-number, which are more generalized notions of the Krawtchouk polynomial 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 Eberlein polynomial over the Johnson scheme. Furthermore, we find another version of the MacWilliams identity over a Hamming scheme.
Keywords
discrete Green's function;P-polynomial scheme;p-number;q-number;Krawtchouk polynomial;Eberlein polynomial;
Language
English
Cited by
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