Cilj istraživanja je konstrukcija novih kombinatoričkih struktura i linearnih kodova s dobrim karakteristikama, posebice LDPC kodova i ekstremalnih Z4-kodova. Kako bi se dobili novi kodovi poželjno je kao polazišnu točku koristiti nove kombinatoričke strukture. Također, iz dobivenih kodova će se konstruirati kombinatoričke strukture (grafovi i dizajni) te proučavati njihova svojstva.

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)

doc. dr. sc Doris Dumičić Danilović (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:

• S. Rukavina, V. D. Tonchev, Extremal ternary self-dual codes of length 36 and symmetric 2-(36, 15, 6) designs with an automorphism of order 2, J. Algebraic Combin. 57 (2023), 905-913.


• D. Crnković, S. Rukavina, M. Šimac, LDPC codes constructed from cubic symmetric graphs,  Appl. Algebra Engrg. Comm. Comput, 33 (2022), 5, 505-522.


• M. Maksimović, S. Rukavina, New regular two-graphs on 38 and 42 vertices, Math. Commun. 27 (2022), 2, 151-161.


• S. Ban, S. Rukavina, Type IV-II codes over Z4 constructed from generalized bent functions, Australasian journal of combinatorics, 84 (2022), 3, 341-356.


• B. Fernández, S. Rukavina, On the 2-Y-homogeneous condition of the incidence graphs of 2-designs, Graphs Combin. 38 (2022), 119, 15 pages


• D. Crnković, S. Rukavina, M. Šimac, LDPC codes from cubic semisymmetric graphs, Ars Math. Contemp. 22 (2022), p. #2.03, 13 pages, doi:10.26493/1855-3974.2501.4c4


• D. Crnković, S. Rukavina, A. Švob, Self-orthogonal codes from equitable partitions of association schemes , J. Algebraic Combin. 55 (2022), 157-171.


• D. Crnković, D. Dumičić Danilović, R. Egan, A. Švob, Periodic Golay pairs and pairwise balanced designs, J. Algebraic Combin. 55 (2022), 245-257.


• D. Crnković, S. Rukavina, New symmetric 2-(71,15,3) designs, Bull. Inst. Combin. Appl. 94 (2022) 79-94.


• D. Crnković, D. Dumičić Danilović, S. Rukavina, On automorphism groups of a biplane (121,16,2), Discrete Math. 344 (2021), 112508, 8 pages


• S. Ban, S. Rukavina, On some new extremal Type II Z4-codes of length 40, Mathematical communications, 25 (2020), 2, 253-268.


• D. Crnković, S. Rukavina, A. Švob, On some distance-regular graphs with many vertices, J. Algebraic Combin. 51 (2020), 641-652.


• S. Ban, D. Crnković, M. Mravić, S. Rukavina, New extremal Type II Z4-codes of length 32 obtained from Hadamard matrices, Discrete Math. Algorithms Appl. 11 (2019), 1950057, 18 pages (electronic) (http://dx.doi.org/10.1142/S1793830919500575).


• D. Crnković, S. Rukavina, M. Šimac, LDPC codes from µ-geodetic graphs obtained from block designs, Graphs Combin. 35 (2019), 451-469.


•  D. Crnković, D. Dumičić Danilović, S. Rukavina, M. Šimac, On some new Steiner 2-designs S(2,5,45), Util. Math. 111 (2019), 281-308.

Radovi prihvaćeni za objavljivanje / Papers accepted for publication:

• S. Ban, S. Rukavina, Construction of self-orthogonal Z₂^k -codes, Des. Codes Cryptogr., to appear


• D. Crnković, M. Mravić, S. Rukavina, Construction of extremal Z4-codes using a neighborhood search algorithm, Adv. Math. Commun., to appear, 18 pages


• M. Maksimović, S. Rukavina, On a construction of self-orthogonal codes from orbit matrices of 2-designs, Contrib. Discrete Math., to appear


• S. Rukavina, V. D. Tonchev, On symmetric 2-(70,24,8) designs with an automorphism of order 6, Glas. Mat., to appear


• D. Crnković, S. Rukavina, A. Švob, Self-orthogonal codes from equitable partitions of distance-regular graphs, Adv. Math. Commun., to appear.

Izlaganja na konferencijama / Talks:

• S. Rukavina, On regular two-graphs on 38 and 42 vertices, Finite Geometry Workshop 2023, Szeged, Hungary, 29.10.2023. - 1.11.2023.


• S. Ban, Construction of self-orthogonal Z₂^k -codes, Finite Geometry and Friends 2023, Brussels, Belgium, 18.09.2023.- 22.09.2023.


• M. Mravić, Some new extremal Z4-codes of lengths 32 and 40, Rijeka Conference on Combinatorial Objects and Their Applications (RICCOTA2023), Rijeka, Hrvatska, 3.7.2023. - 7.7.2023.


• S. Ban, Cyclic self-orthogonal Z₂^k -codes constructed from generalized Boolean functions , Rijeka Conference on Combinatorial Objects and Their Applications (RICCOTA2023), Rijeka, Hrvatska, 3.7.2023. - 7.7.2023.


• S. Rukavina, On extremal ternary self-dual codes of length 36, 10th Slovenian Conference on Graph Theory, Kranjska Gora, Slovenia, 18.6.2023.- 24.6.2023


• S. Rukavina,On extremal ternary self-dual codes of length 36 and related symmetric 2-(36, 15, 6) designs, ALCOCRYPT - ALgebraic and combinatorial methods for COding and CRYPTography, Luminy, France, 20.02.2023. - 24.02.2023.


• D. Dumičić Danilović, Pairwise balanced designs and periodic Golay pairs, 4th Croatian Combinatorial Days Zagreb, Croatia, September 22 - September 23, 2022.


• S. Rukavina , On one property of the incidence graphs of 2-designs, 5th Catania Combinatorial Conference HyGraDe 2022, Catania, Italia, July 6 - July 8, 2022.


• M. Mravić, The search algorithm for extremal Z4-codes, Combinatorial Constructions Workshop, Zagreb, Croatia, June 27 - June 29, 2022.


• S. Ban, Self-orthogonal Z₂^k -codes constructed from Boolean functions, 7th Croatian Mathematical Congress, Split, Croatia, June 15 - June 18, 2022.


• M. Mravić, Modification of the search algorithm for extremal Z4-codes, 7th Croatian Mathematical Congress, Split, Croatia, June 15 - June 18, 2022.


• M. Šimac, LDPC codes and cubic graphs, 7th Croatian Mathematical Congress, Split, Croatia, June 15 - June 18, 2022.


• S. Ban, Self-orthogonal Z₂^k -codes constructed from bent functions, NORCOM 2022 - 14th Nordic Combinatorial Conference, Tromso, Norway, June 7 - June 9, 2022.


• S. Rukavina, On some recent results on biplanes and triplanes, NORCOM 2022 - 14th Nordic Combinatorial Conference, Tromso, Norway, June 7 - June 9, 2022.


• M. Mravić, Search for extremal self-dual Z4-codes, 6th Faculty of Science PhD Symposium, Zagreb, Croatia, April 23 - April 24, 2022.


• S. Rukavina, On the 2-Y -homogeneous condition of the incidence graphs of 2-designs, The Fifty-third Southeastern International Conference on Combinatorics, Graph Theory & Computing, Boca Raton, SAD, March 7 – March 11, 2022.


• S. Ban, A construction of Z4-codes from generalized bent functions, Combinatorial Designs and Codes, Satellite event of the 8th European Congress of Mathematics, Rijeka, Croatia, July 12- July 16, 2021.


• M. Mravić, On extremal self-dual Z4-codes, Combinatorial Designs and Codes, Satellite event of the 8th European Congress of Mathematics, Rijeka, Croatia, July 12- July 16, 2021.


• M. Šimac, On some LDPC codes, Combinatorial Designs and Codes, Satellite event of the 8th European Congress of Mathematics, Rijeka, Croatia, July 12- July 16, 2021.


• S. Rukavina, On some recent results on 2-(v, k, λ) symmetric designs with small λ, 28th British Combinatorial Conference (BCC 2021), Durham, UK, July 5 – July 9, 2021.(https://www.bib.irb.hr/1155835)


• S. Ban, Type IV-II codes over Z4 constructed from generalized bent functions, Graphs and Groups, Geometries and GAP (G2G2) Summer School Satellite event of the 8th European Congress of Mathematics, Rogla, Slovenia, June 27 – July 3, 2021.


• M. Šimac, LDPC codes from cubic semisymmetric graphs, Graphs and Groups, Geometries and GAP (G2G2) Summer School, Satellite event of the 8th European Congress of Mathematics, Rogla, Slovenia, June 27 – July 3, 2021.


• S. Rukavina, A few new triplanes, 8th European Congress of Mathematics, Portorož, Slovenia, June 20-26, 2021.


• S. Rukavina, Self-orthogonal codes from equitable partitions of distance-regular graphs, CanaDam, Canada, May 25-28, 2021.


• S. Rukavina, New extremal Type II Z4-codes of length 32 obtained from Hadamard matrices, 27th British Combinatorial Conference (BCC 2019), Birmingham, UK, July 29 - August 2, 2019.


• M. Mravić, Hadamard matrices and Z4-linear codes, 9th PhD Summer School in Discrete Mathematics, Rogla, Slovenia, June 30 - July 5, 2019.


• M. Šimac, LDPC codes constructed from cubic symmetric graphs, 9th Slovenian Conference on Graph Theory, Bled, Slovenia, June 23 - 29, 2019.


• S. Ban, New extremal Type II Z4-codes of length 32 obtained from Hadamard designs, 9th Slovenian Conference on Graph Theory, Bled, Slovenia, June 23 - 29, 2019.  

Doktorske disertacije / PhD theses:

• S. Ban, Construction of extremal Type II Z4-codes, July 8, 2019.


• M. Mravić, An algorithm for construction of extremal and near- extremal Z4-codes, July 1, 2022.

Bilateralne radionice / Bilateral workshops:

• Bilateralna radionica Designs, codes, graphs and cryptography - an interdisciplinary approach in analysis of certain discrete structures, 10. svibnja 2019. Sažetci predavanja dostupni su na poveznici

Članovi istraživačkog tima izlažu o svojim rezultatima i u okviru Seminara za konačnu matematiku

Zadnje ažurirano: 1.12.2023.