Publication Details

Jennifer Seberry Wallis, Kronecker products and BIBDS, Journal of Combinatorial Theory, Ser. A., 14, (1973), 248-252.


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).