关于奇阶多阶Hadamard矩阵的存在性

2007 3rd International Workshop on Signal Design and Its Applications in Communications Pub Date : 2007-12-26 DOI:10.1109/IWSDA.2007.4408339

Q. K. Trinh, P. Fan, E. Gabidulin, R. N. Mohan

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引用次数: 3

摘要

本文研究了与正交矩阵或正交设计有关的多层(n元)Hadamard矩阵。假定所有的矩阵元素都是整数，这使得二元Hadamard矩阵成为多层(n-ary) Hadamard矩阵的特殊情况。证明了当只包含两个不同的矩阵元素时，存在奇阶的多级Hadamard矩阵;但是，除未知情况外，当所有矩阵元素为连续整数时，不存在奇数阶的多级(n-ary) Hadamard矩阵。

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On the Existence of Multilevel Hadamard Matrices with Odd Order

The multilevel (n-ary) Hadamard matrices, which are related to orthogonal matrices or orthogonal designs, are investigated in this paper. It is assumed that all matrix elements are integers, which make the binary Hadamard matrices as special cases of multilevel (n-ary) Hadamard matrices. It is shown that the multilevel Hadamard matrices of odd order do exist if only two different matrix elements are contained; but, except an unknown case, multilevel (n-ary) Hadamard matrices of odd order do not exist when all matrix elements are successive integers.

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2007 3rd International Workshop on Signal Design and Its Applications in Communications

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