用于将线性码嵌入自正交码的保约束遗传算法

中文摘要 AI 辅助

本文旨在利用最短自正交嵌入方法构造二元最优自正交码。为此，我们设计了一种基于遗传算法的启发式框架，采用基于最小距离和最小重量码字数量的适应度函数，探索最短自正交嵌入的搜索空间。我们构建了“保约束”交叉和变异操作，确保每个染色体都能生成有效的自正交嵌入，同时将高适应度的结构特征（如正交生成元的有利子序列）在各代间传递。我们还分析了该算法的时间和存储复杂度，并通过引导交叉的 ablation 研究，以及在相等时间预算下与随机搜索的对比，验证了设计的有效性。利用该方法，我们得到了66个达到上界的新二元最优自正交码，以及135个达到目前已发现最佳最小距离的自正交码。

英文摘要

In this paper, we aim to construct binary optimal self-orthogonal codes using shortest self-orthogonal embedding methods. For this purpose, we design a heuristic framework based on a genetic algorithm. We explore the search space of shortest self-orthogonal embeddings using a fitness function based on the minimum distance and the number of minimum-weight codewords. We construct \emph{constraint-preserving} crossover and mutation operations so that every chromosome yields a valid self-orthogonal embedding, while high-fitness structural features, such as favorable subsequences of orthogonal generators, are propagated across generations. We also analyze the time and storage complexity of the algorithm, and validate our design through an ablation study on guided crossover and a comparison with random search under an equal time budget. Using this method, we obtain $66$ new binary optimal self-orthogonal codes that meet the upper bound, together with $135$ further self-orthogonal codes attaining the best minimum distance found so far.

发表机构

• Sogang University（西江大学）

机构由 AI 辅助整理，请以论文原文为准。