On the Noncyclic Property of Sylvester Hadamard Matrices
Xiaohu Tang, Udaya Parampalli
IEEE TRANSACTIONS ON INFORMATION THEORY | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC | Published : 2010
In this paper, we are concerned with Hadamard matrices with a certain noncyclic property. First we show that when the first column of a Sylvester Hadamard matrix of order 2m, m ≥ 2, a positive integer, is removed, the number of shift distinct row vectors in the matrix is given by 2m-m. Then, for m ≥ 4, we construct an infinite family of Hadamard matrices with a property that when the first column of the Hadamard matrix is removed, all the row vectors of the matrix are shift distinct. These Hadamard matrices are useful in constructing low correlation zone sequences. © 2010 IEEE.
Awarded by National Science Foundation of China (NSFC)
Manuscript received June 24, 2009; revised February 12, 2010. Date of current version August 18, 2010. X. H. Tang was supported in part by the National Science Foundation of China (NSFC) under Grant 60772086. U. Parampalli was supported in part by the Melbourne Research Grant Scheme 2009 of the University of Melbourne. The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Adelaide, Australia, September 2005, and at the Second International Workshop on Sequence Design and Its Applications to Communications, Yamaguchi, Japan, October 2005.