In this paper, we introduce the notion of Jacobi polynomials of a code with multiple reference vectors, and give the MacWilliams type identity for it. Moreover, we derive a formula to obtain the Jacobi polynomials using the Aronhold polarization operator. Finally, we describe some facts obtained from Type III and Type IV codes that interpret the relation between the Jacobi polynomials and designs.
- Invariant theory
- Jacobi polynomials
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics