An example of an infinitely generated graded ring motivated by coding theory

Abstract

Let $\widetilde{\mathfrak{H}}^{(g)}$ be the graded ring generated by the $r$-th higher weight enumerators of all codes of any length, $1 \leq r \leq g$. In this note we will prove that $\widetilde{\mathfrak{H}}^{(g)}$ is not finitely generated.