Evolving Towards Better Codes: LLM-Guided Search for High-Distance Binary Linear Codes
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,...
| Authors | Amal Seddas, Vladyslav Shashkov, Maryna Viazovska et al. |
|---|---|
| Primary category | cs.IT |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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