发表机构
Aalto University School of Electrical Engineering（阿尔托大学电气工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文对阶数≤32的对称阿达马矩阵按阿达马等价分类，修正了阶数28分类的错误，用新算法完成分类与枚举，还扩展算法到称重矩阵并建立相关理论结果。
AI 中文摘要
本文对阶数不超过32的对称阿达马矩阵按阿达马等价关系进行了分类，特别修正了此前阶数为28的对称阿达马矩阵分类中的错误，还枚举了各阶数下不同对称阿达马矩阵的数量。分类与枚举工作采用了一种新算法，该算法可判定给定阿达马矩阵是否等价于对称阿达马矩阵，文中还描述了该算法向称重矩阵的扩展，并建立了关于对称阿达马矩阵和称重矩阵的理论结果。
英文摘要
In this paper, symmetric Hadamard matrices are classified up to Hadamard equivalence for all orders at most 32. In particular, an error in the previous classification of symmetric Hadamard matrices of order 28 is corrected. The number of distinct symmetric Hadamard matrices at each order is also enumerated. The classification and enumeration are carried out using a new algorithm that determines whether a given Hadamard matrix is equivalent to a symmetric one. The extension of the algorithm to weighing matrices is also described, and theoretical results concerning symmetric Hadamard and weighing matrices are established.
CommentsCorrected the counts of distinct symmetric Hadamard matrices. No other results are changed
