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

Gil Chun Kim, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)509-527
Number of pages19
JournalBulletin of the Korean Mathematical Society
Issue number3
StatePublished - 2013


  • Discrete Green's function
  • Eberlein polynomial
  • Krawtchouk polynomial
  • P-number
  • P-polynomial scheme
  • Q-number


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