迈向更优码：LLM引导的搜索用于高距离二进制线性码
Evolving Towards Better Codes: LLM-Guided Search for High-Distance Binary Linear Codes
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- EPFL（洛桑联邦理工学院）
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中文总结 AI 辅助
本研究利用LLM引导的进化搜索，提出LinCodeEvolve框架，发现七个破纪录的二进制线性码，改进22个表格条目，验证了LLM在编码理论中的有效性。
中文摘要 AI 辅助
由大型语言模型（LLM）驱动的进化程序搜索已在组合数学及其他领域的开放问题上产生了破纪录的构造。我们将此方法应用于改进二进制线性码最佳已知界的长期问题。基于EvoTune进化框架和ShinkaEvolve代码库，我们引入了LinCodeEvolve，它针对精确的最小距离评估器进化码构造程序。策略循环结合了多样性驱动的搜索和专家监督：当进展停滞时，使用新策略来重定向搜索。LinCodeEvolve发现了七个破纪录的码，$[172,21,66]$、$[173,20,68]$、$[176,21,68]$、$[181,21,70]$、$[184,21,72]$、$[189,22,72]$和$[200,21,77]$，其中六个具有简洁的准循环描述。通过标准码修改技术，它们改进了表格中的22个条目。每个码都通过穷举枚举进行了验证。这些结果表明，LLM引导的搜索可以帮助找到改进的码，并补充编码理论中的现有方法。
英文摘要
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.
