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Block designs and self-orthogonal codes constructed from orbit matrices

We present an algorithm for constructing 2- designs admitting a solvable automorphism group. Applying this algorithm, we construct some new Steiner 2-designs S(2, 5, 45) and some new symmetric (78, 22, 6) designs. One of the results is the proof of the nonexistence of (78, 22, 6) difference set in the group Frob_{; ; 39}; ; xZ_2. Further, extending previous results on codes obtained from orbit matrices of 2-designs, we show that under certain conditions both fixed and non-fixed part of an orbit matrix span a self - orthogonal code over the finite field F_{; ; p^n}; ; or the ring Z_m. We construct self-orthogonal codes over Z_4 spanned by orbit matrices of symmetric (78, 22, 6) designs.

Block design ; Steiner 2-design ; Orbit matrix ; Solvable automorphism group ; Difference set ; Self-orthogonal code

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