Machine learning discovers new champion codes

2025/12/15 by Yang‐Hui He, He, Yang-Hui, Alexander Kasprzyk +5
Computer Science · #14G50 (primary) #52B20 #68T07 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Polynomial and algebraic computation #Quantum Computing Algorithms and Architecture

paper · doi:10.48550/arxiv.2512.13370

openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

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.

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