New Constructions of Complete Non-cyclic Hadamard Matrices, Related Function Families and LCZ Sequences

A Hadamard matrix is said to be completely non-cyclic (CNC) if there are no two rows (or two columns) that are shift equivalent in its reduced form. In this paper, we present three new constructions of CNC Hadamard matrices. We give a primary construction using a flipping operation on the submatrices of the reduced form of a Hadamard matrix. We show that, up to some restrictions, the Kronecker product preserves the CNC property of Hadamard matrices and use this fact to give two secondary constructions of Hadamard matrices. The applications to construct low correlation zone sequences are provided.

• Type: Journal
• Year: 2010
• Where: SETA
• Authors: Krystal Guo, Guang Gong
• Keywords: Hadamard, Hadamard Matrices, Hadamard Matrix, Mathematics, SETA 2010