Explicit expression of the Krawtchouk polynomial via a discrete Green's function
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A Krawtchouk polynomial is introduced as the classical Mac-Williams identity, which can be expressed in weight-enumerator-free formof a linear code and its dual code over a Hamming scheme. In thispaper 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 adiscrete Green’s function. As corollaries, we obtain a new expression ofthe Krawtchouk polynomial over the Hamming scheme and the Eber-lein polynomial over the Johnson scheme. Furthermore, we find anotherversion of the MacWilliams identity over a Hamming scheme.
Abstract
A Krawtchouk polynomial is introduced as the classical Mac-Williams identity, which can be expressed in weight-enumerator-free formof a linear code and its dual code over a Hamming scheme. In thispaper 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 adiscrete Green’s function. As corollaries, we obtain a new expression ofthe Krawtchouk polynomial over the Hamming scheme and the Eber-lein polynomial over the Johnson scheme. Furthermore, we find anotherversion of the MacWilliams identity over a Hamming scheme.
참고문헌 (9)
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