大语言模型引导发现重量五二元自行车码

中文摘要 AI 辅助

基于我们先前由大语言模型（LLM）引导的程序进化工作流程，我们研究了重量五的二元自行车（BB）码和扰动二元自行车（PBB）码。由此产生的目录包含1,142个不同的码提案，其中1,081个非基线提案归因于LLM生成的程序。在整个目录中，我们验证了连通的Calderbank--Shor--Steane（CSS）实现[[96,4,10]]、[[140,6,10]]和[[180,4,14]]。搜索后比较验证了七个导入的Lin--Pryadko档案构造。对于该档案中也存在的领先参数三元组，我们提供了精确距离证据、显式二元表示和验证的组件约简。基于基无关的连通性分析确定了1,142个目录条目中的409个为不连通，并显示具有精确距离证书的类别中73.1%包含重复的连通组件。代数分析将连通的CSS类别组织为3阶、7阶和15阶分圆核层。最强的精确连通PBB参数点是[[216,4,10]]，由两个不同的组件类别达到。在LLM引导活动中记录的936个不同CSS提案中，具有正距离的816个（87.18%）被认证为$d\geq5$。作为比较，三个随机搜索对照组各均匀无放回地采样6,444个CSS码提案，使用与LLM引导活动相同的每格和编码维度样本计数。在这些对照中，4,672--4,785个提案（72.50--74.26%）满足相同标准。LLM引导活动具有更高的认证产出，而随机对照覆盖更多连通类别。总之，这些结果将LLM引导发现扩展到更受约束的码族，并对其最强候选提供了可复现的结构和精确距离说明。

英文摘要

Building on our earlier program-evolution workflow guided by large language models (LLMs), we study weight-five bivariate bicycle (BB) and perturbed bivariate bicycle (PBB) codes. The resulting catalogue contains 1,142 distinct code proposals, including 1,081 nonbaseline proposals attributable to LLM-generated programs. Across the catalogue, we certify connected Calderbank--Shor--Steane (CSS) realizations [[96,4,10]], [[140,6,10]], and [[180,4,14]]. A post-search comparison certifies seven imported Lin--Pryadko archive constructions. For leading parameter triples also represented in that archive, we provide exact distance evidence, explicit bivariate presentations, and verified component reductions. A basis-independent connectivity analysis identifies 409 of the 1,142 catalogue entries as disconnected and shows that 73.1\% of the classes with exact distance certificates contain repeated connected components. Algebraic analysis organizes the connected CSS classes into order-3, order-7, and order-15 cyclotomic-kernel strata. The strongest exact connected PBB parameter point is [[216,4,10]], attained by two distinct component classes. Among the 936 distinct CSS proposals from the LLM-guided campaign with a recorded positive distance, 816 (87.18\%) are certified at $d\geq5$. For comparison, three random-search controls each sample 6,444 CSS code proposals uniformly without replacement, using the same per-lattice and encoded-dimension sample counts as the LLM-guided campaign. In these controls, 4,672--4,785 proposals (72.50--74.26\%) meet the same criterion. The LLM-guided campaign has the higher certified yield, while the random controls cover more connected classes. Together, these results extend LLM-guided discovery to a more constrained code family and provide a reproducible structural and exact-distance account of its strongest candidates.

发表机构

• IBM Research（IBM研究院）

机构由 AI 辅助整理，请以论文原文为准。