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

2026-09-29

AI Summary

This study addresses the challenge of surpassing the best known distance bounds for binary linear codes by proposing LinCodeEvolve, a framework that integrates large language model-guided evolutionary search with exact evaluation to optimize construction programs. A policy loop mechanism is introduced to effectively overcome search stagnation through diversity-driven exploration and expert supervision. Building upon the EvoTune framework and the ShinkaEvolve codebase, this work discovers seven record-breaking linear codes and improves twenty-two tabulated entries, with all results rigorously verified via exhaustive search. By demonstrating how generative AI can systematically advance combinatorial optimization in coding theory, this research establishes a new paradigm for AI-driven exploration of theoretical boundaries in error-correcting code design.

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.

Problem

• binary linear codes
• minimum distance
• coding theory
• LLM-guided search

Innovation

• LLM-guided evolutionary search
• binary linear codes
• minimum distance
• program synthesis
• quasi-cyclic codes