Naslov
On construction of 2-designs and related self- orthogonal codes

Autori
Dumičić Danilović, Doris ; Crnković, Dean ; Rukavina, Sanja

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
6th Croatian Mathematical Congress / - , 2016, 1-1

Skup
6th Croatian Mathematical Congress

Mjesto i datum
Zagreb, Hrvatska, 14.06.2016. - 17.06.2016

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Tactical decomposition of design ; Automorphism group ; Self-orthogonal code ; Binary linear code

Sažetak
We describe a method for constructing 2-designs admitting a solvable automorphism group using tactical decomposition of design, and construct new symmetric (78, 22, 6) designs. Besides that, we show that up to isomorphism there is exactly one symmetric (78, 22, 6) design admitting an automorphism group isomorphic to Frob_39×Z_2, namely the design constructed by Zvonimir Janko and Tran van Trung. This result implies the nonexistence of a (78, 22, 6) difference set in the group Frob_39×Z_2. In this talk we show that under certain conditions both fixed and non-fixed part of an orbit matrix span a self-orthogonal code over the finite field F_{;p^n}; or over the ring Z_m. Further, we study binary linear codes spanned by incidence matrices of the constructed designs.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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