Craigen introduced and studied signed group Hadamard matrices extensively, following Craigen's lead, studied and provided a better estimate for the asymptotic existence of signed group Hadamard matrices and consequently improved the asymptotic existence of Hadamard matrices. In this paper, we introduce and study signed group orthogonal designs (SODs). The main results include a method for finding SODs for any k-tuple of positive integer and then an application to obtain orthogonal designs from SODs, namely, for any k-tuple (u1,u2,...,uk) of positive integers, we show that there is an integer N = N(u1, u2,...,uk) such that for each n ≥ N, a full orthogonal design (no zero entries) of type (2nu1,2nu2,...,2nuk) exists.
Signed group orthogonal designs and their applications / Ghaderpour, Ebrahim. - 133:(2015), pp. 107-123. (Intervento presentato al convegno Workshop on Algebraic Design Theory and Hadamard Matrices tenutosi a University of Lethbridge) [10.1007/978-3-319-17729-8_9].
Signed group orthogonal designs and their applications
Ebrahim Ghaderpour
2015
Abstract
Craigen introduced and studied signed group Hadamard matrices extensively, following Craigen's lead, studied and provided a better estimate for the asymptotic existence of signed group Hadamard matrices and consequently improved the asymptotic existence of Hadamard matrices. In this paper, we introduce and study signed group orthogonal designs (SODs). The main results include a method for finding SODs for any k-tuple of positive integer and then an application to obtain orthogonal designs from SODs, namely, for any k-tuple (u1,u2,...,uk) of positive integers, we show that there is an integer N = N(u1, u2,...,uk) such that for each n ≥ N, a full orthogonal design (no zero entries) of type (2nu1,2nu2,...,2nuk) exists.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
