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Machine Learning Discovers New Champion Codes

Q Le, Yang‐Hui He, Dmitrii Riabchenko +1 more

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 a best minimum Hamming distance. 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, Algebraic--Geometry, and potentially quantum 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 a best minimum Hamming distance. 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, Algebraic--Geometry, and potentially quantum codes.

Jul 29, 20250 citations

Binary Linear Codes That Are Optimal for Error Correction

Torleiv Kløve

Lecture notes in computer scienceJan 1, 20063 citations

Machine learning discovers new champion codes

Yang‐Hui He, Alexander Kasprzyk, Q Le +1 more

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.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.

arXiv:2512.13370npj Artificial IntelligenceMar 25, 20260 citations

Uncorrectable errors of weight half the minimum distance for binary linear codes

憲司安永, Yasunaga, Kenji

Jul 1, 20080 citations

Upper Bound on Correcting Partial Random Errors

Ankita Gaur, Bhu Dev Sharma

Abstract Since coding has become a basic tool for practically all communication/electronic devices, it is important to carefully study the error patterns that actually occur. This allows correction of only partial errors rather than those which have been studied using Hamming distance, in non-binary cases. The paper considers a class of distances, SK-distances, in terms of which partial errors can be defined. Examining the sufficient condition for the existence of a parity check matrix for a given number of parity-checks, the paper contains an upper bound on the number of parity check digits for linear codes with property that corrects all partial random errors of an (n, k ) code with minimum SK-distance at least d. The result generalizes the rather widely used Varshamov-Gilbert bound, which follows from it as a particular case.Abstract Since coding has become a basic tool for practically all communication/electronic devices, it is important to carefully study the error patterns that actually occur. This allows correction of only partial errors rather than those which have been studied using Hamming distance, in non-binary cases. The paper considers a class of distances, SK-distances, in terms of which partial errors can be defined. Examining the sufficient condition for the existence of a parity check matrix for a given number of parity-checks, the paper contains an upper bound on the number of parity check digits for linear codes with property that corrects all partial random errors of an (n, k ) code with minimum SK-distance at least d. The result generalizes the rather widely used Varshamov-Gilbert bound, which follows from it as a particular case.

Cybernetics and Information TechnologiesSep 1, 20131 citation

Error Correcting Ability of Linear Block Codes

辰一小島

群馬大学教育学部紀要. 自然科学編Jan 1, 19890 citations

Linear Binary Error Correcting Codes with Specified Minimum Hamming Distance

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