Abstract

In 1976, Kramer and Mesner observed that finding a t-design with a given automorphism group can be reduced to solving a matrix problem of the form AX=M, X[i]=0 or I, for all i, I<=i<=n, where A is an m by n positive integer matrix built from the required automorphism group and M is a particular m dimensional integer vector. This problem is NP-complete. We present an algorithm that searches for a solution when given an instance of This 0-1 matrix problem. This algorithm always halts in polynomial time but does not always find a solution when one exists. The problem is first converted to one of finding a particular short vector in a lattice and then uses a lattice basis reduction algorithm due to A.K. Lenstra, H.W. Lenstra and L. Lovasz [9] to attempt to find it. We apply this method to the search for simple t-designs with t>=6 and duplicate the results of Leavitt, Kramer and Magliveras [3,10] in substantially shorter time. Furthermore, a new simple 6-design was found using the algorithm described in this paper

Publication Date

1986

Comments

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type

Article

Department, Program, or Center

Center for Advancing the Study of CyberInfrastructure

Campus

RIT – Main Campus

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