engleski

Block designs and strongly regular graphs constructed from some linear and unitary groups

Block designs and strongly regular graphs are constructed with incidence expressed in terms of maximal subgroups of unitary groups U(4, 2) and U(3, 3) and linear groups L(2, 32) and L(2, 49). We show that a symmetric (45, 12, 3) design and two symmetric (40, 13, 4) designs can be constructed from the group U(4, 2). A symmetric (36, 15, 6) design and two symmetric (63, 31, 15) designs can be constructed from the unitary group U(3, 3). Furthermore, we describe a construction of 2-(28, 12, 11), 2-(28, 4, 1) and 2-(36, 16, 12) designs from U(3, 3). We have constructed two isomorphic 2-(50, 8, 4) designs from the linear group L(2, 49). We also describe a construction of a strongly regular graph with parameters (528, 62, 31, 4) from the linear group L(2, 32). The group from which the incidence structure is constructed acts transitively on the structure.

block design; strongly regular graph; linear group; unitary group

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