Quasi-symmetric designs and self-dual codes
In this paper the author once again successfully applies results on self- orthogonal codes to show that three designs based on S(5,8,24), namely 2- (21,6,4), 2-(21,7,12) and 2-(22,7,16) [cf. \textit{J. M. Goethals} and \textit{J. J. Seidel}, Can. J. Math. 22, 597-614 (1970; Zbl 0198.293)], are unique up to isomorphism. \textit{A. Neumaier} [Lect. Notes Math. 969, 258- 275 (1982; Zbl 0497.05014)] gave a list of so-called exceptional parameter sets for quasi-symmetric designs with 2k\(\leq v\leq 40\). It is shown that two of these designs, namely 2-(28,7,16) and 2-(29,7,12), do not exist. The proof is based on the classification of certain self-dual codes given by \textit{V. Pless} [IEEE Trans. Inform. Theory IT-24, 738-746 (1978; Zbl 0387.94010)]. We remark that Neumaier's list was recently extended to 2k\(\leq v\leq 70\) [c.f. \textit{R. Calderbank}, J. Comb. Theory, Ser. A 47 (1988)].
scientific article; zbMATH DE number 4047736