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## On triplanes of order twelve admitting an automorphism of order six and their binary and ternary codes

Crnković, Dean; Rukavina, Sanja; Simčić, Loredana
On triplanes of order twelve admitting an automorphism of order six and their binary and ternary codes // Utilitas mathematica, 103 (2017), 23-40 (međunarodna recenzija, članak, znanstveni)

Naslov
On triplanes of order twelve admitting an automorphism of order six and their binary and ternary codes

Autori
Crnković, Dean ; Rukavina, Sanja ; Simčić, Loredana

Izvornik
Utilitas mathematica (0315-3681) 103 (2017); 23-40

Ključne riječi
triplane, automorphism group ; orbit matrix ; linear code ; k-geodetic graph

Sažetak
In this paper we present the complete classification of triplanes (71, 15, 3) admitting an action of the cyclic automorphism group of order six. Up to isomorphism there are 146 such triplanes and these are all triplanes of order 12 known up to now. Further, we analyze binary and ternary codes spanned by the incidence matrices of triplanes (71, 15, 3) and their residual designs. The constructed binary codes are self- complementary, and the ternary codes are self- orthogonal. In addition, we study ternary self-orthogonal codes constructed from the orbit matrices for Z_3 acting on the 146 symmetric 2-(71, 15, 3) designs. Some of the obtained codes have minimum distance one or two less than the best known codes with the same length and dimension. Finally, we discuss k-geodetic graphs from the symmetric (71, 15, 3) designs and their residual and derived designs.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
HRZZ-IP-2013-11-1637 - Kodovi i s njima povezane kombinatoričke strukture (Dean Crnković, )

Ustanove
Tehnički fakultet, Rijeka,
Sveučilište u Rijeci - Odjel za matematiku

Profili:

Sanja Rukavina (autor)

Dean Crnković (autor)

Loredana Simčić (autor)

#### Citiraj ovu publikaciju

Crnković, Dean; Rukavina, Sanja; Simčić, Loredana
On triplanes of order twelve admitting an automorphism of order six and their binary and ternary codes // Utilitas mathematica, 103 (2017), 23-40 (međunarodna recenzija, članak, znanstveni)
Crnković, D., Rukavina, S. & Simčić, L. (2017) On triplanes of order twelve admitting an automorphism of order six and their binary and ternary codes. Utilitas mathematica, 103, 23-40.
@article{article, year = {2017}, pages = {23-40}, keywords = {triplane, automorphism group, orbit matrix, linear code, k-geodetic graph}, journal = {Utilitas mathematica}, volume = {103}, issn = {0315-3681}, title = {On triplanes of order twelve admitting an automorphism of order six and their binary and ternary codes}, keyword = {triplane, automorphism group, orbit matrix, linear code, k-geodetic graph} }

#### Časopis indeksira:

• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus

#### Uključenost u ostale bibliografske baze podataka:

• MathSciNet
• Zentrallblatt für Mathematik/Mathematical Abstracts