About Code Equivalence -- a Geometric Approach

TL;DR

This paper introduces geometric algorithms for testing the equivalence of linear codes by relating them to multisets of points in projective geometry, aiding in classification and analysis.

Contribution

It presents a novel geometric approach to code equivalence testing, connecting linear codes with projective geometry structures.

Findings

Algorithms effectively determine code equivalence using geometric methods

The approach simplifies classification of linear codes

Potential for improved bounds in combinatorial structures

Abstract

The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for equivalence of linear codes, based on their relation to multisets of points in a projective geometry.