Designs, strongly regular graphs and codes constructed from some primitive groups (CROSBI ID 42782)
Prilog u knjizi | izvorni znanstveni rad
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
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
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