Naslov
Some optimal codes and strongly regular graphs from the linear group L(4, 3)

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

Izvornik
UTILITAS MATHEMATICA (0315-3681) 89 (2012); 237-255

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
strongly regular graph; symmetric design; self-orthogonal design; self-orthogonal code; automorphism group

Sažetak
We construct self-orthogonal codes obtained from the row span over GF(2) or GF(3) of the incidence (resp. adjacency) matrices of some self-orthogonal designs (resp. strongly regular graphs) defined by the action of the simple linear group L(4, 3) on the conjugacy classes of several of its maximal subgroups. We use the geometry of the designs or graphs and give an account on the codewords of several weights. Further, we show that the codes with parameters [27, 23, 3]_3, [27, 4, 18]_3, [27, 17, 6]_3, [40, 29, 6]_3, [117, 91, 6]_2, [117, 97, 6]_3, and [130, 111, 4]_3 are all optimal. In addition, we obtain a self-dual [80, 40, 12] code invariant under L(4, 3).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA