Symmetric (36,15,6) design having U(3,3) as an automorphism group

Up to isomorphism there are four symmetric (36,15,6) designs with automorphisms of order 7. Full automorphism group of one of them is the Chevalley group G(2,2) = U(3,3) : Z2 of order 12096. Unitary group U(3,3) acts transitively on that design

Symmetric (36,15,6) design having U(3,3) as an automorphism group

Up to isomorphism there are four symmetric (36,15,6) designs with automorphisms of order 7. Full automorphism group of one of them is the Chevalley group G(2,2) = U(3,3) : Z2 of order 12096. Unitary group U(3,3) acts transitively on that design

Some symmetric (47,23,11) designs

Up to isomorphism there are precisely fifty-four symmetric designs with parameters (47,23,11) admitting a faithful action of a Frobenius group of order 55. From these fifty-four designs one can construct 179 pairwise nonisomorphic 2-(23,11,10) designs as derived and 191 pairwise nonisomorphic 2-(24,12,11) designs as residual designs. We have determined full automorphism groups of all constructed designs. One of 2-(24,12,11) designs has full automorphism group of order 15840, isomorphic to the group M11 × 2, acting transitively on the set of points

On symmetric (36,15,6) designs

Up to isomorphism there are 4 symmetric (36,15,6) designs with automorphisms of order 7 and 38 symmetric (36,15,6) designs with automorphisms of order 5. For those designs full automorphism groups are determined. Also, all symmetric (36,15,6) designs having automorphisms of order 3 acting with 9 and 6 fixed points, or cyclic automorphism groups of order 4 acting standardly are constructed and orders of their full automorphism groups are determined

Binary doubly-even self-dual codes of length 72 with large automorphism groups

We study binary linear codes constructed from fifty-four Hadamard 2-(71,35,17) designs. The constructed codes are self-dual, doubly-even and self-complementary. Since most of these codes have large automorphism groups, they are suitable for permutation decoding. Therefore we study PD-sets of the obtained codes. We also discuss error-correcting capability of the obtained codes by majority logic decoding. Further, we describe a construction of a strongly regular graph with parameters (126,25,8,4) from a binary [35,8,4] code related to a derived 2-(35,17,16) design

Symmetric (70,24,8) designs having Frob21 × Z2 as an automorphism group

Up to isomorphism there are twenty-two symmetric (70,24,8) designs having automorphism group isomorphic to Frob21 × Z2. Among them there are four self-dual, and nine pairs of dual designs. Full automorphism groups of those designs are isomorphic to Frob21 × Z2. Designs are constructed by means of tactical decompositions, using a principal series of the group Frob21 × Z2

Codes from orbit matrices of strongly regular graphs

We show that under certain conditions submatrices of orbit matrices of strongly regular graphs span self-orthogonal codes. In order to demonstrate this method of construction, we construct self-orthogonal binary linear codes from orbit matrices of the triangular graphs T(2k) with at most 120 vertices. Further, we obtain strongly regular graphs and block designs from codewords of the constructed codes

Intriguing sets of strongly regular graphs and their related structures

In this paper we outline a technique for constructing directed strongly regular graphs by using strongly regular graphs having a "nice" family of intriguing sets. Further, we investigate such a construction method for rank three strongly regular graphs having at most $45$ vertices. Finally, several examples of intriguing sets of polar spaces are provided

Enumeration of symmetric (45,12,3) designs with nontrivial automorphisms

We show that there are exactly 4285 symmetric (45,12,3) designs that admit nontrivial automorphisms. Among them there are 1161 self-dual designs and 1562 pairs of mutually dual designs. We describe the full automorphism groups of these designs and analyze their ternary codes. R. Mathon and E. Spence have constructed 1136 symmetric (45,12,3) designs with trivial automorphism group, which means that there are at least 5421 symmetric (45,12,3) designs. Further, we discuss trigeodetic graphs obtained from the symmetric $(45,12,3)$ designs. We prove that $k$-geodetic graphs constructed from mutually non-isomorphic designs are mutually non-isomorphic, hence there are at least 5421 mutually non-isomorphic trigeodetic graphs obtained from symmetric $(45,12,3)$ designs