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

arXiv: https://arxiv.org/abs/2609.37056 · HTML: https://mlsanity.com/paper/2609.37056/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 36 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 13 of 13)

- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [Automated Design of Agentic Systems](https://mlsanity.com/paper/2408.08435/) (2024)
- [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://mlsanity.com/paper/2509.19349/) (2025)
- [Evolution through Large Models](https://mlsanity.com/paper/2206.08896/) (2022)
- [Language Model Crossover: Variation through Few-Shot Prompting](https://mlsanity.com/paper/2302.12170/) (2023)
- [Evolutionary Computation in the Era of Large Language Model: Survey and Roadmap](https://mlsanity.com/paper/2401.10034/) (2024)
- [Constructions in combinatorics via neural networks](https://mlsanity.com/paper/2104.14516/) (2021)
- [Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learning](https://mlsanity.com/paper/2504.05108/) (2025)
- [PatternBoost: Constructions in Mathematics with a Little Help from AI](https://mlsanity.com/paper/2411.00566/) (2024)
- [LLM-Guided Search for Deletion-Correcting Codes](https://mlsanity.com/paper/2504.00613/) (2025)
- [Mutation Without Variation: Convergence Dynamics in LLM-Driven Program Evolution](https://mlsanity.com/paper/2606.05408/) (2026)

## 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.