Abstract:For each integer $k \in [0,9]$, we count the number of plane cubic curves defined over a finite field $\mathbb{F}_q$ that do not share a common component and intersect in exactly $k\ \mathbb{F}_q$-rational points. We set this up as a problem about a weight enumerator of a certain projective Reed-Muller code. The main inputs to the proof include counting pairs of cubic curves that do share a common component, counting configurations of points that fail to impose independent conditions on cubics, and a variation of the MacWilliams theorem from coding theory.
From: Nathan Kaplan [view email]
[v1]
Tue, 31 Mar 2020 04:00:33 UTC (31 KB)
[v2]
Mon, 10 May 2021 22:41:00 UTC (31 KB)
[v3]
Wed, 22 Jul 2026 21:48:29 UTC (31 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。