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.
KeywordsHadamard matrices completely non-cyclic type low correlation zone sequences shift-distinctness
Unable to display preview. Download preview PDF.
- 2.Craigen, R.: Hadamard matrices and designs. In: Colbourn, C.J., Dinitz, J.H. (eds.) CRC Handbook of Combinatorial Designs, pp. 370–377. CRC Press, Boca Raton (1996)Google Scholar
- 6.Guo, K., Gong, G.: New constructions of complete non-cyclic hadamard matrices, related function families and lcz sequences. Technical Report, University of Waterloo, CACR 2010-14 (2010)Google Scholar
- 13.Tang, X.H., Udaya, P.: New recursive construction of low correlation zone sequences. In: Proceedings of Second Int. Workshop Sequence Design and Its Applications to Communication, Shimonoseki, Japan, October 10-14 (2005)Google Scholar