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.
Original language | English |
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Pages (from-to) | 509-527 |
Number of pages | 19 |
Journal | Bulletin of the Korean Mathematical Society |
Volume | 50 |
Issue number | 3 |
DOIs | |
State | Published - 2013 |
Keywords
- Discrete Green's function
- Eberlein polynomial
- Krawtchouk polynomial
- P-number
- P-polynomial scheme
- Q-number