Kronecker Products and BIBDs

Recursive constructions are given which permit, under conditions described in the paper, a (v, b, r, k, lambda)configuration to be used to obtain a (v', b', r', k, lambda)-configuration. Although there are many equivalent definitions we will mean by a (v, b, r, k, lambda)-configuration or BIBD that (0, 1)-matrix A of size v x b with row sum r and column sum k satisfying AAT = (r lambda)I + lambdaJ where, as throughout the remainder of this paper, I is the identity matrix and J the matrix with every element +1 whose sizes should be determined from the context or by a subscript ( Jn is square of order n). Disciplines Physical Sciences and Mathematics Publication Details Jennifer Seberry Wallis, Kronecker products and BIBDS, Journal of Combinatorial Theory, Ser. A., 14, (1973), 248-252. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/946 Reprinted from JOURNAL OF COMBINATORIAL THEORY All Rights Reserved by Academic Press, N ew York and London Note Vol. 14, No.2, March 1973 Printed in Belgium Kronecker Products and BIBDs