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Evolving Towards Better Codes: LLM-Guided Search for High-Distance Binary Linear Codes

arXiv 2609.37056 ↗First posted 29 Sep 2026cs.IT cs.AI cs.NEcited by 0

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Abstract (arXiv)

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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References · 13

  1. 2024The AI Scientist: Towards Fully Automated Open-Ended Scientific Discoverycited by 1,002
  2. 2025AlphaEvolve: A coding agent for scientific and algorithmic discoverycited by 763
  3. 2015Illuminating search spaces by mapping elitescited by 406
  4. 2024Automated Design of Agentic Systemscited by 360
  5. 2025ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolutioncited by 146
  6. 2022Evolution through Large Modelscited by 131
  7. 2023Language Model Crossover: Variation through Few-Shot Promptingcited by 119
  8. 2024Evolutionary Computation in the Era of Large Language Model: Survey and Roadmapcited by 89
  9. 2021Constructions in combinatorics via neural networkscited by 46
  10. 2025Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learningcited by 39
  11. 2024PatternBoost: Constructions in Mathematics with a Little Help from AIcited by 32
  12. 2025LLM-Guided Search for Deletion-Correcting Codescited by 4
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  1. 2026Mutation Without Variation: Convergence Dynamics in LLM-Driven Program Evolutioncited by 4

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