Geometry of the Minimum Distance

John Pawlina; Stefan Tohaneanu

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arXiv · 2310.00102

Geometry of the Minimum Distance

John Pawlina·Stefan Tohaneanu

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Abstract

Let ${\mathbb K}$ be any field, let $X\subset {\mathbb P}^{k-1}$ be a set of $n$ distinct ${\mathbb K}$-rational points, and let $a\geq 1$ be an integer. In this paper we find lower bounds for the minimum distance $d(X)_a$ of the evaluation code of order $a$ associated to $X$. The first results use $\alpha(X)$, the initial degree of the defining ideal of $X$, and the bounds are true for any set $X$. In another result we use $s(X)$, the minimum socle degree, to find a lower bound for the case when $X$ is in general linear position. In both situations we improve and generalize known results.

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BibTeX RIS

John Pawlina, Stefan Tohaneanu. 2023-09-29. Geometry of the Minimum Distance. https://arxiv.org/abs/2310.00102

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