On the Noncyclic Property of Sylvester Hadamard Matrices

Abstract

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.