Designs, strongly regular graphs and codes constructed from some primitive groups
Crnkovi cacute Dean, Mikuli cacute Crnkovi cacute Vedrana, Rodrigues B.G. · NATO science for peace and security series. D, Information and communication security · 2011
Let G be a finite group acting primitively on the sets &OHgr;1and &OHgr;2. We describe a construction of 1-designs with block set &OHgr;1and block set &OHgr;2, having G as an automorphism group. Applying this construction method we obtain a unital 2-(q3+1, q+1, 1), and a semi-symmetric (q4−q3+q2, q2−q, (1)) from the unitary group U3(q), where q = 3, 4, 5, 7. From the unital and the semi-symmetric design we build a projective plane PG(2, q2). Further, we describe other combinatorial structures constructed from these unitary groups and structures constructed from U4(2), U4(3) and L2(49).