Classification of (16,6,2)-designs by ovals
The three biplanes of order four (i.e. with \(k=6)\) have received a number of treatments, the first by Hussain forty years ago. Algebraic coding theory brought the ovals of these designs into prominence and the reviewer and \textit{C. Salwach} [Int. J. Math. Math. Sci. 2, 261-281 (1979; Zbl 0424.05009)] treated them from that point of view. (The authors seem not to have aware of that treatment and their methods are entirely combinatorial.) They give an ab initio development of these designs showing along the way that such a design contains 12, 28, or 60 ovals and that there is precisely one such design in each case. The treatment is elementary (but not straightforward) and gives a new approach to these designs. The methods are intrinsic to the parameter set and do not generalize. Such generalization as is available arises out of algebraic coding theory, the ovals being the minimal-weight vectors in the dual code. In Theorem 5.4 read ''deleting'' for ''detecting''.
scientific article; zbMATH DE number 3873338
scientific article