Weight enumerators, intersection enumerators and Jacobi polynomials II
Himadri Shekhar Chakraborty, Tsuyoshi Miezaki, Manabu Oura

TL;DR
This paper introduces Jacobi polynomials and intersection enumerators for codes over finite fields and rings, explores their interrelations, and establishes MacWilliams type identities, advancing algebraic coding theory.
Contribution
It presents new definitions of Jacobi polynomials and intersection enumerators for codes over various algebraic structures, and derives MacWilliams identities relating them.
Findings
Defined Jacobi polynomials for codes over $\\mathbb{F}_q$ and $\mathbb{Z}_k$
Established interrelations among these polynomials and enumerators
Proved MacWilliams type identities for Jacobi polynomials
Abstract
In the present paper, we introduce the concepts of Jacobi polynomials and intersection enumerators of codes over and for arbitrary genus . We also discuss the interrelation among them. Finally, we give the MacWilliams type identities for Jacobi polynomials.
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Taxonomy
TopicsCoding theory and cryptography · Advanced Algebra and Geometry · Finite Group Theory Research
