Naslov
Enumeration of symmetric (45,12,3) designs with nontrivial automorphisms

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

Izvornik
Journal of Algebra Combinatorics Discrete Structures and Applications (2148-838X) 3 (2016), 3; 145-154

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

Ključne riječi
symmetric design ; linear code ; automorphism group ; k-geodetic graph

Sažetak
We show that there are exactly 4285 symmetric (45, 12, 3) designs that admit nontrivial automorphisms. Among them there are 1161 self- dual designs and 1562 pairs of mutually dual designs. We describe the full automorphism groups of these designs and analyze their ternary codes. R. Mathon and E. Spence have constructed 1136 symmetric (45, 12, 3) designs with trivial automorphism group, which means that there are at least 5421 symmetric (45, 12, 3) designs. Further, we discuss trigeodetic graphs obtained from the symmetric (45, 12, 3) designs. We prove that k-geodetic graphs constructed from mutually non- isomorphic designs are mutually non-isomorphic, hence there are at least 5421 mutually non-isomorphic trigeodetic graphs obtained from symmetric (45, 12, 3) designs.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA