论文标题
部分可观测时空混沌系统的无模型预测
Constructions and restrictions for balanced splittable Hadamard matrices
论文作者
论文摘要
如果其行的某个子集具有每两个不同列的点乘积最多占两个值的dot乘积，则Hadamard矩阵是平衡分配的。该定义是由Kharaghani和Suda在2019年引入的，尽管以前已经使用不同的术语研究了等效的配方。我们以平衡的可拆分hadamard矩阵，真正的平面等距离紧密帧，球形两距离套件和两距离紧密框架来整理先前的结果。我们使用组合分析来限制可拆分的Hadamard矩阵的参数，以分为几个类别之一，并在其相互关系上获得强烈的新约束。确定这些类别的一个重要考虑因素是与平衡的可拆分hadamard矩阵相关的强界图是原始的还是不符合的。我们在原始案例和不当案例中构建了新的无限型Hadamard矩阵的家族。基础差分集中的部分差异集的包装提供了丰富的示例来源，我们从中构建了hadamard矩阵，承认行分解，以使平衡的可分配属性同时与分解的每个集合的每个结合。
A Hadamard matrix is balanced splittable if some subset of its rows has the property that the dot product of every two distinct columns takes at most two values. This definition was introduced by Kharaghani and Suda in 2019, although equivalent formulations have been previously studied using different terminology. We collate previous results phrased in terms of balanced splittable Hadamard matrices, real flat equiangular tight frames, spherical two-distance sets, and two-distance tight frames. We use combinatorial analysis to restrict the parameters of a balanced splittable Hadamard matrix to lie in one of several classes, and obtain strong new constraints on their mutual relationships. An important consideration in determining these classes is whether the strongly regular graph associated with the balanced splittable Hadamard matrix is primitive or imprimitive. We construct new infinite families of balanced splittable Hadamard matrices in both the primitive and imprimitive cases. A rich source of examples is provided by packings of partial difference sets in elementary abelian 2-groups, from which we construct Hadamard matrices admitting a row decomposition so that the balanced splittable property holds simultaneously with respect to every union of the submatrices of the decomposition.
