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

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

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
Information Security, Coding Theory and Related Combinatorics

Urednik/ci
Crnković, Dean ; Tonchev, Vladimir

Izdavač
IOS Press

Grad
Amsterdam

Godina
2011

Raspon stranica
231-252

ISBN
978-1-60750-662-1

Ključne riječi
design, strongly regular graph, code, primitive simple group

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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