Evolving Towards Better Codes: LLM-Guided Search for High-Distance Binary Linear Codes
Abstract
Evolutionary program search driven by large language models (LLMs) has produced record-breaking constructions for open problems in combinatorics and beyond. We apply this approach to the longstanding problem of improving the best-known bounds for binary linear codes. Building on the EvoTune evolutionary framework and the ShinkaEvolve codebase, we introduce LinCodeEvolve, which evolves code-construction programs against an exact minimum-distance evaluator. A strategy loop combines diversity-driven search and expert supervision: when progress plateaus, new strategies are used to redirect the search. LinCodeEvolve discovers seven record-breaking codes, $[172,21,66]$, $[173,20,68]$, $[176,21,68]$, $[181,21,70]$, $[184,21,72]$, $[189,22,72]$ and $[200,21,77]$, six of which have concise quasi-cyclic descriptions. With standard code modification techniques, they improve $22$ entries of the tables. Every code is verified by exhaustive enumeration. These results suggest that LLM-guided search can help find improved codes and complement existing methods in coding theory.
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BibTeX
@misc{seddas2026evolving,
title = {{Evolving Towards Better Codes: LLM-Guided Search for High-Distance Binary Linear Codes}},
author = {Amal Seddas and Vladyslav Shashkov and Maryna Viazovska and Emmanuel Abbe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37056},
eprint = {2609.37056},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37056},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Evolving Towards Better Codes: LLM-Guided Search for High-Distance Binary Linear Codes
AU - Amal Seddas
AU - Vladyslav Shashkov
AU - Maryna Viazovska
AU - Emmanuel Abbe
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37056
UR - https://arxiv.org/abs/2609.37056
AB - Evolutionary program search driven by large language models (LLMs) has produced record-breaking constructions for open problems in combinatorics and beyond. We apply this approach to the longstanding problem of improving the best-known bounds for binary linear codes. Building on the EvoTune evolutionary framework and the ShinkaEvolve codebase, we introduce LinCodeEvolve, which evolves code-construction programs against an exact minimum-distance evaluator. A strategy loop combines diversity-driven search and expert supervision: when progress plateaus, new strategies are used to redirect the search. LinCodeEvolve discovers seven record-breaking codes, $[172,21,66]$, $[173,20,68]$, $[176,21,68]$, $[181,21,70]$, $[184,21,72]$, $[189,22,72]$ and $[200,21,77]$, six of which have concise quasi-cyclic descriptions. With standard code modification techniques, they improve $22$ entries of the tables. Every code is verified by exhaustive enumeration. These results suggest that LLM-guided search can help find improved codes and complement existing methods in coding theory.
ER -