A polynomial time reduction from the multi-graph isomorphism problem to additive code equivalence

TL;DR

This paper introduces a polynomial time reduction from the multi-graph isomorphism problem to additive code equivalence over finite fields, linking graph theory and coding theory.

Contribution

It provides the first known polynomial time reduction connecting multi-graph isomorphism to additive code equivalence, expanding the understanding of computational complexity in coding theory.

Findings

Establishes a polynomial time reduction between multi-graph isomorphism and additive code equivalence.

Bridges concepts between graph isomorphism and coding theory.

Potentially impacts complexity classification of related problems.

Abstract

We present a polynomial time reduction from the multi-graph isomorphism problem to the problem of code equivalence of additive codes over finite extensions of ${\mathbb F}_2$.