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Oct. 2003 An example of an infinitely generated graded ring motivated by coding theory
Manabu Oura
Proc. Japan Acad. Ser. A Math. Sci. 79(8): 134-135 (Oct. 2003). DOI: 10.3792/pjaa.79.134

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.

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Manabu Oura. "An example of an infinitely generated graded ring motivated by coding theory." Proc. Japan Acad. Ser. A Math. Sci. 79 (8) 134 - 135, Oct. 2003. https://doi.org/10.3792/pjaa.79.134

Information

Published: Oct. 2003
First available in Project Euclid: 18 May 2005

zbMATH: 1050.11102
MathSciNet: MR2013093
Digital Object Identifier: 10.3792/pjaa.79.134

Subjects:
Primary: 11T71 , 94B05

Keywords: code , graded ring , higher weight enumerator , weight enumerator

Rights: Copyright © 2003 The Japan Academy

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Vol.79 • No. 8 • Oct. 2003
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