Nodal surfaces in $\mathbb{P}^3$ and coding theory

To each nodal hypersurface one can associate a binary linear code. Here we show that the binary linear code associated to sextics in $\mathbb{P}^3$ with the maximum number of $65$ nodes, as e.g. the Barth sextic, is unique. We also state possible candidates for codes that might be associated with a hypothetical septic attaining the currently best known upper bound for the maximum number of nodes.

Institutions

Publication Details

Journal
ArXiv.org
Published
2025-05-23
Primary Topic
Coding theory and cryptography
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Nodal surfaces in $\mathbb{P}^3$ and coding theory

ArXiv.org
Coding theory and cryptography
article

Nodal surfaces in $\mathbb{P}^3$ and coding theory

article en

Abstract

To each nodal hypersurface one can associate a binary linear code. Here we show that the binary linear code associated to sextics in $\mathbb{P}^3$ with the maximum number of $65$ nodes, as e.g. the Barth sextic, is unique. We also state possible candidates for codes that might be associated with a hypothetical septic attaining the currently best known upper bound for the maximum number of nodes.

ArXiv.org
University of Bayreuth (DE)
Openalex Percentile: Top 73%
Coding theory and cryptography
Open Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Nodal surfaces in $\mathbb{P}^3$ and coding theory · ArXiv.org (2025) | TGRS Research Map | TGRS