On a linear code from a configuration of affine lines

TL;DR

This paper introduces a method to construct linear codes from affine line configurations and proposes a new decoding algorithm leveraging this geometric structure, demonstrating promising effectiveness.

Contribution

It presents a novel way to derive linear codes from affine line arrangements and introduces an innovative decoding algorithm based on geometric configurations.

Findings

Effective decoding algorithm demonstrated

New class of linear codes constructed from affine lines

Potential improvements in decoding efficiency

Abstract

We will show how to obtain a linear code from a configuration of affine lines in general position and a suitable set of rational points. We will also explain a new decoding algorithm based on the configuration, which seems to be quite effective.