Kombinatoričke strukture i linearni kodovi, kao i njihove međusobne veze, predmet su mnogih aktualnih istraživanja. Cilj predloženog projekta je dati daljnji doprinos istraživanjima u navedenom području, pri čemu će se posebno istraživati distancijsko biregularni grafovi i Z_2k kodovi, njihova svojstva, metode konstrukcije i međusobne veze. Često se kombinatoričke strukture i kodovi isprepliću na način da egzistencija jednog od tih objekata omogućuje konstrukciju drugog. Zbog toga ćemo istraživati i međusobne veze distancijsko biregularnih grafova i Z_2k kodova, povezanost njihovih svojstava, kao i mogućnost konstrukcije jednog od njih pomoću drugih.

Combinatorial structures and linear codes and their interrelationships are the subject of much current research. The aim of the proposed project is to further contribute to research in the aforementioned field, and in particular to study distance biregular graphs and Z_2k codes, their properties, construction methods and mutual connections. Often combinatorial structures and codes are so interwoven that the existence of one of them enables the construction of the other. For this reason, we will study the mutual connections of distance biregular graphs and Z_2k codes, the interconnection of their properties, and the possibility of constructing one with the help of the other.

Voditelj / Principal investigator:

prof. dr. sc. Sanja Rukavina (Fakultet za matematiku Sveučilišta u Rijeci / Faculty of Mathematics, University of Rijeka)
e-mail: sanjar@math.uniri.hr

Istraživački tim / Research team:

doc. dr. sc. Sara Ban (Fakultet za matematiku Sveučilišta u Rijeci / Faculty of Mathematics, University of Rijeka)

izv. prof. Marija Maksimović (Fakultet za matematiku Sveučilišta u Rijeci / Faculty of Mathematics, University of Rijeka)

dr. sc. Matteo Mravić (Fakultet za matematiku Sveučilišta u Rijeci / Faculty of Mathematics, University of Rijeka)

doc. dr. sc. Marina Šimac (Fakultet za matematiku Sveučilišta u Rijeci / Faculty of Mathematics, University of Rijeka)

Objavljeni radovi / Papers:

• Rukavina, Sanja; Tonchev, Vladimir D., Symmetric 2-(36,15,6) designs with an automorphism of order two, Journal of combinatorial designs, 32 (2024), 10; 606-624. doi: 10.1002/jcd.21952


• Crnković, Dean; Mravić, Matteo; Rukavina, Sanja, Construction of extremal Z4-codes using a neighborhood search algorithm, Advances in mathematics of communications, 19 (2025), 1; 91-108. doi: 10.3934/amc.2023039

Izlaganja na konferencijama / Talks:

• Rukavina, Sanja; Tonchev, Vladimir D. Self-dual (near-)extremal ternary codes and combinatorial 2-designs, Combinatorial Constructions Conference Dubrovnik, Hrvatska, 07.04.2024-13.04.2024


• Ban Martinović, Sara; Rukavina, Sanja, New extremal Type II Z4-codes via doubling method, 8th Croatian Mathematical Congress Osijek, Hrvatska, 02.07.2024-05.07.2024


• Maksimović, Marija; Fernandez, Blas; Rukavina, Sanja, Characterizing bipartite distanceregularized graphs with vertices of eccentricity at most 4, 5th Croatian Combinatorial Days, Zagreb, Hrvatska, 19.09.2024-20.09.2024