Explicit expression of the krawtchouk polynomial via a discrete green's function
- 주제(키워드) Discrete Green's function , Eberlein polynomial , Krawtchouk polynomial , P-number , P-polynomial scheme , Q-number
- 관리정보기술 faculty
- 등재 SCIE, KCI등재, SCOPUS
- 발행기관 Taehan Suhakhoe
- 발행년도 2013
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000095492
- 본문언어 영어
- Published As http://dx.doi.org/10.4134/JKMS.2013.50.3.509
초록/요약
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.
more