On self-orthogonal designs and codes related to Held's simple group (CROSBI ID 254527)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Crnković, Dean ; Mikulić Crnković, Vedrana ; Rodrigues, Bernardo G.
engleski
On self-orthogonal designs and codes related to Held's simple group
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).
Design ; orbit matrix ; linear code ; sporadic simple group ; Held group
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Podaci o izdanju
12 (3)
2018.
607-628
objavljeno
1930-5346
1930-5338
10.3934/amc.2018036