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Designs, strongly regular graphs and codes constructed from some primitive groups (CROSBI ID 42782)

Prilog u knjizi | izvorni znanstveni rad

Crnković, Dean ; Mikulić Crnković, Vedrana ; Rodrigues, B. G. Designs, strongly regular graphs and codes constructed from some primitive groups // Information Security, Coding Theory and Related Combinatorics / Crnković, Dean ; Tonchev, Vladimir (ur.). Amsterdam: IOS Press, 2011. str. 231-252

Podaci o odgovornosti

Crnković, Dean ; Mikulić Crnković, Vedrana ; Rodrigues, B. G.

engleski

Designs, strongly regular graphs and codes constructed from some primitive groups

Let G be a finite group acting primitively on the sets $\Omega_1$ and $\Omega_2.$ We describe a construction of 1-designs with block set $\Omega_1$ and block set $\Omega_2, $ having G as an automorphism group. Applying this construction method we obtain a unital 2-(q^3+1, q+1, 1), and a semi-symmetric (q^4-q^3+q^2, q^2 - q, (1)) from the unitary group U(3, q), where q =3, 4, 5, 7. From the unital and the semi-symmetric design we build a projective plane PG(2, q^2). Further, we describe other combinatorial structures constructed from these unitary groups and structures constructed from U(4, 2), U(4, 3) and L(2, 49). We also construct self-orthogonal codes obtained from the row span over GF(2) or GF(3) of the incidence (resp. adjacency) matrices of mostly self-orthogonal designs (resp. strongly regular graphs) defined by the action of the simple unitary groups U(3, q) for q=3, 4, 7 and U(4, q) for q=2, 3 and the linear group L(2, 49) on the conjugacy classes of some of their maximal subgroups. Some of the codes are optimal or near optimal for the given length and dimension.

design, strongly regular graph, code, primitive simple group

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Podaci o prilogu

231-252.

objavljeno

Podaci o knjizi

Information Security, Coding Theory and Related Combinatorics

Crnković, Dean ; Tonchev, Vladimir

Amsterdam: IOS Press

2011.

978-1-60750-662-1

Povezanost rada

Matematika