In this paper, we introduce the notion of the complete joint Jacobi polynomial of two linear codes of length n over Fq and Zk. We give the MacWilliams type identity for the complete joint Jacobi polynomials of codes. We also introduce the concepts of the average Jacobi polynomial and the average complete joint Jacobi polynomial over Fq and Zk. We give a representation of the average of the complete joint Jacobi polynomials of two linear codes of length n over Fq and Zk in terms of the compositions of n and its distribution in the codes. Further we present a generalization of the representation for the average of the (g+ 1) -fold complete joint Jacobi polynomials of codes over Fq and Zk. Finally, we give the notion of the average Jacobi intersection number of two codes.
- Jacobi polynomials
- Weight enumerators
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Applied Mathematics