Naslov
On self-orthogonal designs and codes related to Held's simple group

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

Izvornik
Advances in mathematics of communications (1930-5346) 12 (2018), 3; 607-628

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

Ključne riječi
Design ; orbit matrix ; linear code ; sporadic simple group ; Held group

Sažetak
A construction of designs acted on by simple primitive groups is used to find some 1-designs and associated self-orthogonal, decomposable and irreducible codes that admit the simple group He of Held as an automorphism group. The properties of the codes are given and links with modular representation theory are established. Further, we introduce a method of constructing self-orthogonal binary codes from orbit matrices of weakly self-orthogonal designs. Furthermore, from the support designs of the obtained self-orthogonal codes we construct strongly regular graphs with parameters (21, 10, 3, 6), (28, 12, 6, 4), (49, 12, 5, 2), (49, 18, 7, 6), (56, 10, 0, 2), (63, 30, 13, 15), (105, 32, 4, 12), (112, 30, 2, 10) and (120, 42, 8, 18).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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