Abstract
It is shown that quasi-symmetric designs which are derived or residual designs of nonisomorphic symmetric designs with the symmetric difference property are also nonisomorphic. Combined with a result by W. Kantor, this implies that the number of nonisomorphic quasi-symmetric designs with the symmetric difference property grows exponentially. The column spaces of the incidence matrices of these designs provide an exponential number of inequivalent codes meeting the Grey-Rankin bound. A transformation of quasi-symmetric designs by means of maximal arcs is described. In particular, a residual quasi-symmetric design with the symmetric difference property is transformed into a quasi-symmetric design with the same block graph but higher rank over GF(2).
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Communicated by R.C. Mullin
Dedicated to Professor Hanfried Lenz on the occasion of his 75th birthday.
This paper was written while the author was at the University of Giessen as a Research Fellow of the Alexander von Humboldt Foundation, on leave from the University of Sofia, Bulgaria.
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Jungnickel, D., Tonchev, V.D. Exponential number of quasi-symmetric SDP designs and codes meeting the Grey-Rankin bound. Des Codes Crypt 1, 247–253 (1991). https://doi.org/10.1007/BF00123764
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DOI: https://doi.org/10.1007/BF00123764