51、107和115维阿达马最大行列式问题的新记录
New Records for the Hadamard Maximal Determinant Problem
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中文总结 AI 辅助
该研究针对51、107、115维±1矩阵行列式的阿达马最大问题，计算出新下界并提供对应矩阵构建数据，提升了相关记录。
中文摘要 AI 辅助
我们计算了阶数n=51、n=107和n=115的±1矩阵行列式的新下界，分别较之前的记录提高了3.1%、0.44%和1.68%，并提供了构建这些矩阵所需的数据。
英文摘要
The Hadamard maximal determinant problem seeks an $n\times n$ matrix $X$ with entries in $\{\pm 1\}$, which maximizes the determinant $\vert \det X \vert$ for a given order $n \in \mathbb{N}$. We report matrices attaining new record determinants for orders $n\equiv 3\pmod{4}$ between $103$ and $119$, as well as $n=51$. We provide a proof of optimality within a specific family of circulant--block constructions for $X$. For these orders, we recast the Hadamard problem as a sequence reconstruction problem from a pair of periodic autocorrelation functions, subject to certain arithmetic conditions. We describe several learning--based strategies for reconstruction and provide a comparison with classical simulated annealing--style approaches as a benchmark.
发表机构
- California Institute of Technology（加州理工学院）
- University of Cambridge（剑桥大学）
- London Institute for Mathematical Sciences（伦敦数学科学研究所）
- University of Miami（迈阿密大学）
- Temple University（天普大学）
机构由 AI 辅助整理，请以论文原文为准。
