Title :
On the Existence of Multilevel Hadamard Matrices with Odd Order
Author :
Trinh, Quang Khai ; Fan, Pingzhi ; Gabidulin, Ernst M. ; Mohan, R.N.
Author_Institution :
Southwest Jiaotong Univ., Chengdu
Abstract :
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.
Keywords :
Hadamard matrices; information theory; multilevel Hadamard matrices; n-ary Hadamard matrices; odd order; orthogonal designs; orthogonal matrices; Communication systems; Digital audio players; Discrete cosine transforms; Error correction; Error correction codes; Irrigation; Linear algebra; Mathematics; Matrix decomposition; Moon; multilevel Hadamard matrix; orthogonal design; orthogonal matrix;
Conference_Titel :
Signal Design and Its Applications in Communications, 2007. IWSDA 2007. 3rd International Workshop on
Conference_Location :
Chengdu
Print_ISBN :
978-1-4244-1074-3
Electronic_ISBN :
978-1-4244-1074-3
DOI :
10.1109/IWSDA.2007.4408339
