A class of Steiner 4-wise balanced designs derived from Preparata codes

The minimum weight codewords in the Preparata code of length n = 4 m are utilized for the construction of an innnite family of Steiner S(4; f5; 6g; 4 m + 1) designs for any m 2. A t-wise balanced design with parameters t-(v; K;) is a pair (X; B) where X is a set of v points and B is a collection of subsets of X (called blocks) with sizes from the set K, such that every t-subset of X is contained in exactly blocks. If jKj=1, that is, all blocks are of the same size, say k, the design is a t-(v; k;) design. A Steiner design (or system) is a design with = 1. The notation S(t; K; v) (resp. S(t; k;)) is often used in this case. There has been recent interest in Steiner t-wise balanced designs, motivated by the lack of any known innnite family of Steiner systems S(t; k; v) for t 4 3]. In 3] Kramer and Mathon studied t-wise balanced Steiner designs on v 16 points and their extensions.