Codes and matrices in studies on designs (Q909660)

This paper investigates methods based on codes and matrices for determining the existence or non-existence of certain designs. Hamada and Kobayashi made the first steps in this direction. This is a sequel to a paper of the author, \textit{R. Roth, G. H. J. van Rees} and \textit{S. A. Vanstone} [J. Comb. Theory, Ser. A 47, No.2, 157-175 (1988; Zbl 0661.05015)]. Even though the methods are general, they are applied to the particular case of a (22,33,12,8,4) design. The MacWilliams identity was used to examine the existence or non-existence of (22,33,12,8,4) design. Still to settle the existence or non-existence of (22,33,12,8,4) design something further will have to be added to the methods mentioned in this paper.