Machine learning discovers new champion codes

TL;DR

This paper introduces a novel machine learning approach combining transformers and genetic algorithms to efficiently discover champion linear error-correcting codes with optimal minimum Hamming distances.

Contribution

It presents a new method that leverages machine learning and evolutionary algorithms to identify high-performance codes, reducing search complexity and expanding code discovery.

Findings

Successfully identified new champion codes across various classes.

Reduced search space for discovering optimal codes.

Applicable to classical and quantum error-correcting codes.

Abstract

Linear error-correcting codes form the mathematical backbone of modern digital communication and storage systems, but identifying champion linear codes (linear codes achieving or exceeding the best known minimum Hamming distance) remains challenging. By training a transformer to predict the minimum Hamming distance of a class of linear codes and pairing it with a genetic algorithm over the search space, we develop a novel method for discovering champion codes. This model effectively reduces the search space of linear codes needed to achieve champion codes. Our results present the use of this method in the study and construction of error-correcting codes, applicable to codes such as generalised toric, Reed-Muller, Bose-Chaudhuri-Hocquenghem, algebrogeometric, and potentially quantum codes.