Y. He

A. Kasprzyk

Q. Le

D. Riabchenko

Machine learning finds “champion” codes by predicting and optimising their minimum Hamming distance, a measure of a code’s robustness.

Linear error-correcting codes underpin digital communication and data storage, but finding new “champion” codes that achieve or exceed the best known minimum Hamming distances remains challenging. Here, a transformer trained to predict code performance is combined with a genetic algorithm to guide the search. By dramatically reducing the space of possibilities, the method discovers many new champion linear codes.

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.

Machine learning discovers new champion codes