Monimial Matrix Analogue of Yoshida's theorem

TL;DR

This paper generalizes weight enumerator concepts for linear codes over finite fields, establishing a monomial matrix analogue of Yoshida's theorem and extending identities to multiple code combinations.

Contribution

It introduces a monomial matrix analogue of Yoshida's theorem for average complete joint weight enumerators of linear codes over finite fields.

Findings

Derived MacWilliams type identities for generalized weight enumerators.

Established a monomial matrix analogue of Yoshida's theorem.

Presented a generalized representation for average g-fold complete joint weight enumerators.

Abstract

In this paper, we study variants of weight enumerators of linear codes over $\mathbb{F}_q$. We generalize the concept of average complete joint weight enumerators of two linear codes over $\mathbb{F}_q$. We also give its MacWilliams type identities. Then we establish a monomial analogue of Yoshida's theorem for this average complete joint weight enumerators. Finally, we present the generalized representation for average of $g$-fold complete joint weight enumerators for $\mathbb{F}_q$-linear codes and establish a monomial matrix analogue of Yoshida's theorem for average $g$-fold complete joint weight enumerators.