Uniri projekt / UNIRI project

Kodovi, grupe i kombinatoričke strukture / Codes, groups and combinatoral structures

Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka
 

Fakultet za matematiku

Sveučilište u Rijeci
 

 

U sklopu ovog projekta konstruirat će se i analizirati različiti tipovi kombinatoričkih dizajna i grafova, kao i kodovi određeni njihovim matricama incidencije i matricama susjedstva, odnosno orbitnim matricama. Kombinatoričke strukture konstruirat će se kombiniranjem algebarskih i geometrijskih metoda te uz primjenu računala. Proučavat će se i drugi kombinatorički objekti, kao što su binarni komplementarni nizovi (npr. periodični Golayjevi parovi) i Hadamardove matrice (uključujući kompleksne Hadamardove matrice). Također će se proučavati veza s drugim strukturama, na primjer s konačnim geometrijama i asocijacijskim shemama. Konačne grupe imat će značajnu ulogu u konstrukciji i analizi kombinatoričkih struktura. Kao rezultate predloženog istraživanja očekujemo konstrukcije i klasifikacije različitih tipova kombinatoričkih dizajna i grafova (npr. novih blokovnih dizajna i jako regularnih, odnosno distance-regularnih, grafova) i drugih kombinatoričkih objekata (komplementarnih nizova, Hadamardovih matrica, itd.), kao i konstrukciju kodova s dobrim svojstvima (npr. linearnih kodova s velikom minimalnom udaljenošću s obzirom na duljinu i dimenziju koda, samoortogonalnih odnosno samodualnih kodova, itd.). Očekujemo da će rezultati ovog projekta biti zanimljivi znanstvenicima koji rade u području teorije dizajna, teorije kodiranja i teorije grafova, kao i onima koji se bave istraživanjima u području teorije konačnih grupa.

This project deals with construction and analysis of various types of combinatorial designs and graphs, as well as codes determined by their incidence or adjacency matrices, or their orbit matrices. For construction of combinatorial structures we will combine computational, geometric and algebraic approach. We will also take into consideration other combinatorial objects, such as binary complementary sequences (e.g. periodic Golay pairs) and Hadamard matrices (including complex Hadamard matrices). Relations to other structures (finite geometries, association schemes, etc.) will also be taken into account. Finite groups actions will have a significant role in constructing and analysing combinatorial structures. As a result of the proposed research, we expect a construction and classification of various types of combinatorial designs and graphs (e.g. new block designs and strongly/distance regular graphs) and other combinatorial objects (complementary sequences, Hadamard matrices, etc.), as well as a construction of codes with good properties (e.g. linear codes with large minimum distance comparing to the length and the dimension of the code, self-orthogonal or self-dual codes, etc.). We expect that the outcomes of this project will be of interest for researchers working in design theory, coding theory and graph theory, and for those working in theory of finite groups.

 

Voditelj / Principal investigator:

prof. dr. sc. Dean Crnković (Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka ), e-mail: deanc@math.uniri.hr

Istraživački tim / Research team:

dr. sc. Ana Grbac (Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka)

doc. dr. sc. Daniel Hawtin (Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka)

doc. dr. sc. Marija Maksimović (Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka)

doc. dr. sc. Nina Mostarac (Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka)

izv. prof. dr. sc. Andrea Švob (Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka)

dr. sc. Tin Zrinski (Fakultet za matematiku, Sveučilište u Rijeci / Faculty of Mathematics, University of Rijeka)

 

Objavljeni radovi / Papers:

  • D. Crnković, F. Pavese, A. Švob, Intriguing sets of strongly regular graphs and their related structures, Contrib. Discrete Math. 18 (2023), 66–89.

  • M. Shi, Y. Li, W. Cheng, D. Crnković, D. Krotov, P. Solé, Self-dual bent sequences for complex Hadamard matrices, Des. Codes Cryptogr. 91 (2023), 1453–1474.

  • M. Shi, Y. Li, W. Cheng, D. Crnković, D. Krotov, P. Solé, Self-dual Hadamard bent sequences, J. Syst. Sci. Complex. 36 (2023), 894-908.

  • D. Crnković, A. Grbac, A. Švob, Formally self-dual LCD codes from two-class association schemes, Appl. Algebra Engrg. Comm. Comput. 34 (2023), 183-200.

  • D. Crnković, V. Mikulić Crnković, A. Švob, Construction of transitive q-analogs of designs, Math. Comput. Sci. 17 (2023), Paper No. 2, 5 pages.

  • R. F. Bailey, D. R. Hawtin, On the classification of binary completely transitive codes with almost-simple top-group, European J. Combin. 107 (2023), 103604, 28 pp.

  • M. Maksimović, On Some Regular Two-Graphs up to 50 Vertices, Symmetry 15 (2023), 408.

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

  • D. Crnković, A. Švob, Switching for 2-designs, Des. Codes Cryptogr. 90 (2022), 1585-1593.

  • D. Crnković, D. R. Hawtin, A. Švob, Neighbour-transitive codes and partial spreads in generalised quadrangles, Des. Codes Cryptogr. 90 (2022), 1521-1533.

  • D. Crnković, T. Zrinski, Constructing block designs with a prescribed automorphism group using genetic algorithm, J. Combin. Des. 30 (2022), 515-526.

  • D. Crnković, S. Rukavina, M. Šimac, LDPC codes from cubic semisymmetric graphs, Ars Math. Contemp. 22 (2022), #P2.03, 13 pages.

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

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

  • D. Crnković, A. Švob, New constructions of divisible design Cayley graphs, Graphs Combin. 38 (2022), 17, 8 pages.

  • D. R. Hawtin, J. Lansdown, The non-existence of block-transitive subspace designs, Combinatorial Theory 2, No. 1 (2022), Paper No. 11, 13 pp.

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

  • D. Crnković, A. Švob, New symmetric 2-(176,50,14) designs, Discrete Math. 344 (2021), 112623, 3 pages.

  • D. R. Hawtin, s-Elusive codes in Hamming graphs, Des. Codes Cryptogr. 89 (2021), 1211-1220.

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

  • D. Crnković, N. Mostarac, B. G. Rodrigues, L. Storme, s-PD-sets for codes from projective planes PG(2,2h), 5 ≤ h ≤ 9, Adv. Math. Commun. 15 (2021), 423-440.

  • D. Crnković, R. Egan, B. G. Rodrigues, A. Švob, LCD codes from weighing matrices, Appl. Algebra Engrg. Comm. Comput. 32 (2021), 175–189.

  • D. Crnković, A. Švob, V. D. Tonchev, Strongly regular graphs with parameters (81,30,9,12) and a new partial geometry,  J. Algebraic Combin. 53 (2021), 253-261.

  • D. Crnković, A. Švob, Application of tolerance graphs to combat COVID-19 pandemic, SN Comput. Sci. 2 (2021), 83, 8 pages.

  • R. F. Bailey, D. R. Hawtin, On the 486-vertex distance-regular graphs of Koolen-Riebeek and Soicher, Electron. J. Combin. 27 (2020), #P3.13, 12 pages.

  • D. Crnković, R. Egan, A. Švob, Self-orthogonal codes from orbit matrices of Seidel and Laplacian matrices of strongly regular graphs, Adv. Math. Commun. 14 (2020), 591-602.

  • D. Crnković, M. Maksimović, Strongly regular graphs with parameters (37,18,8,9) having nontrivial automorphisms, Art Discrete Appl. Math. 3 (2020), #P2.10, 8 pages.

  • J. D'haeseleer, J. Mannaert, L. Storme, A. Švob, Cameron-Liebler line classes in AG(3,q), Finite Fields Appl. 67 (2020) 101706, 17 pages.

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

  • D. Crnković, M. Maksimović, Construction of strongly regular graphs having an automorphism group of composite order, Contrib. Discrete Math. 15 (2020), 22-41.

  • D. Crnković, F. Pavese, A. Švob, On the PSU(4,2)-invariant vertex-transitive strongly regular (216,40,4,8) graph, Graphs Combin. 36 (2020), 503-513.

  • D. Crnković, H. Kharaghani, A. Švob, Divisible design Cayley digraphs, Discrete Math. 343 (2020), 111784, 8 pages.

  • A. Švob, Transitive distance-regular graphs from linear groups L(3,q), q=2,3,4,5, Trans. Comb. 9 (2020), 49-60.

  • M. Maksimović, Self-orthogonal codes from row orbit matrices of strongly regular graphs, Sarajevo J. Math. 15 (2019), 309-322.

  • 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).

  • A. Švob, Transitive distance-regular graphs from the unitary groups U(3,4), U(4,3) and U(5,2), Bull. Inst. Combin. Appl. 87 (2019), 103-113.

  • D. Crnković, A. Švob, V. Tonchev, Cyclotomic trace codes, Algorithms, 12 (2019) 168, 10 pages (electronic) (https://doi.org/10.3390/a12080168).

  • M. De Boeck, M. Rodgers, L. Storme, A. Švob, Cameron-Liebler sets of generators in finite classical polar spaces, J. Combin. Theory Ser. A 167 (2019), 340-388.

  • 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.

  • D. Crnković, A. Švob, Transitive t-designs and strongly regular graphs constructed from linear groups L(2,q), q <= 23, Int. J. Group Theory 8 (2019), 43-64.

  • D. Crnković, V. Mikulić Crnković, A. Švob, Block designs and strongly regular graphs admitting a transitive action of the Mathieu group M11, Australas. J. Combin. 73 (2019), 149-161.

  • D. Crnković, R. Egan, A. Švob, Constructing self-orthogonal and Hermitian self-orthogonal codes via weighing matrices and orbit matrices, Finite Fields Appl. 55 (2019), 64-77.

 

Pozvana predavanja / Invited talks:  

  • D. Crnković, Construction of transitive q-designs and q-graphs, Workshop ""Groups, graphs and everything in between", Bled, Slovenia, May 4-7, 2023.

  • A. Švob, LCD subspace codes, Workshop on Combinatorics in Digital Communication, Eindhoven University of Technology, Eindhoven, Netherlands, April 19-21, 2023.

  • D. Crnković, Application of Tolerance Graphs to Combat COVID-19 Pandemic, World Biological Science and Technology Conference 2022, Osaka, Japan, online, July 20-22, 2022.

  • A. Švob, Switching for 2-designs, Minisymposium: Designs and Algebraic Structures, 29th British Combinatorial Conference, Lancaster, UK, July 11-15, 2022.

  • D. Crnković, Pairwise balanced designs and periodic Golay pairs, Minisymposium: Designs and Algebraic Structures, 29th British Combinatorial Conference, Lancaster, UK, July 11-15, 2022.

  • A. Švob, Divisible design Cayley graphs and digraphs, Combinatorial Constructions Workshop, Zagreb, Croatia, June 27-29, 2022.

  • A. Švob, On some constructions of divisible design Cayley graphs and digraphs, 24th Conference of the International Linear Algebra Society, Minisymposium on Designs and Codes, Galway, Ireland, June 20-24, 2022.

  • D. Crnković, q-ary strongly regular graphs, 24th Conference of the International Linear Algebra Society, Minisymposium on Designs and Codes, Galway, Ireland, June 20-24, 2022.

  • D. Crnković, q-ary strongly regular graphs, The 5th Workshop on Algebraic Graph Theory and its Applications, Akademgorodok, Russia, November 1 - 5, 2021.

  • A. Švob, Codes from orbit matrices of Seidel and Laplacian matrices of strongly regular graphs, The 5th Workshop on Algebraic Graph Theory and its Applications, Akademgorodok, Russia, November 1 - 5, 2021.

  • D. Crnković, Divisible design Cayley graphs and digraphs, The 4th Workshop on Algebraic Graph Theory and its Applications, Akademgorodok, Russia, March 1 - 7, 2021.

  • A. Švob, Transitive distance-regular graphs and related codes, The 4th Workshop on Algebraic Graph Theory and its Applications, Akademgorodok, Russia, March 1 - 7, 2021.

  • D. Crnković, New constructions of Deza digraphs, The 3rd Workshop on Algebraic Graph Theory and its Applications, Akademgorodok, Russia, November 2 - 8, 2020.

  • A. Švob, Strongly regular graphs with parameters (81,20,9,12) and a new partial geometry, The 3rd Workshop on Algebraic Graph Theory and its Applications, Akademgorodok, Russia, November 2 - 8, 2020.

 

Izlaganja na konferencijama / Talks:  

  • T. Zrinski, Application of genetic algorithms in constructions of block designs and strongly regular graphs from orbit matrices, Workshop on Combinatorics in Digital Communication, Eindhoven University of Technology, Eindhoven, Netherlands, April 19-21, 2023.

  • D. Crnković, Pairwise balanced designs related to Periodic Golay pairs, 39th Colloqium on Combinatorics, KolKom2022, Paderborn, Germany, 18-19 November, 2022.

  • A. Švob, LCD codes from equitable partitions of association schemes, 39th Colloqium on Combinatorics, KolKom2022, Paderborn, Germany, 18-19 November, 2022.

  • A. Švob, Switching for 2-designs and examples, 2022 Combinatorics, Computing, Group Theory and Applications in South Florida, Florida, USA, August 14-21, 2022.

  • D. Hawtin, Neighbour-transitive codes in Kneser graphs, 29th British Combinatorial Conference, Lancaster, UK, July 11-15, 2022.

  • M. Maksimović, Regular two-graphs from strongly regular graphs, 5th Catania Combinatorial Conference HyGraDe 2022, Catania, Italy, July 6-8, 2022.

  • D. Crnković, Switching for 2-designs and Hadamard matrices, Combinatorial Constructions Workshop, Zagreb, Croatia, June 27-29, 2022.

  • D. Hawtin, Neighbour-transitive codes in generalised quadrangles, Combinatorial Constructions Workshop, Zagreb, Croatia, June 27-29, 2022.

  • M. Maksimović, New regular two-graphs on 38 and 42 vertices, Combinatorial Constructions Workshop, Zagreb, Croatia, June 27-29, 2022.

  • A. Grbac, On some results about LCD codes based on two-class association schemes, 7th Split mathematical congress, Split, Croatia, June 15-18, 2022.

  • N. Mostarac, DRGs and new block designs obtained from the Mathieu groups, 7th Split mathematical congress, Split, Croatia, June 15-18, 2022.

  • D. Hawtin, Non-existence of block-transitive subspace designs, 7th Split mathematical congress, Split, Croatia, June 15-18, 2022.

  • M. Maksimović, Construction of strongly regular graphs having an automorphism group of composite order, 7th Split mathematical congress, Split, Croatia, June 15-18, 2022.

  • T. Zrinski, Constructions of block designs from orbit matrices using a modified genetic algorithm, 7th Split mathematical congress, Split, Croatia, June 15-18, 2022.

  • A. Švob, Pairwise balanced designs and periodic Golay pairs, 43rd Australasian Combinatorics Conference, Melbourne, Australia, December 13 -17, 2021.

  • A. Švob, Strongly regular graphs with parameters (81,30,9,12) and a new partial geometry, The 64th Annual Congress of the South African Mathematical Society, SAMS 2021, South Africa, November 29 - December 1, 2021.

  • D. Crnković, Construction of transitive q-designs, 26th International Conference on Applications of Computer Algebra, online, July 23 - 27, 2021.

  • A. Grbac, On some constructions of LCD codes, Combinatorial Designs and Codes (CDC 2021), Rijeka, Croatia, July 12 - 16, 2021.

  • D. Hawtin, Neighbour-transitive codes in generalised quadrangles, Combinatorial Designs and Codes (CDC 2021), Rijeka, Croatia, July 12 - 16, 2021.

  • N. Mostarac, Distance-regular graphs from the Mathieu groups, Combinatorial Designs and Codes (CDC 2021), Rijeka, Croatia, July 12 - 16, 2021.

  • T. Zrinski, S(2,5,45) designs constructed from orbit matrices using a modified genetic algorithm, Combinatorial Designs and Codes (CDC 2021), Rijeka, Croatia, July 12 - 16, 2021.

  • A. Švob, Distance-regular graphs obtained from the Mathieu groups and new block designs, 28th British Combinatorial Conference (BCC 2021), Durham, United Kingdom, July 5 - 9, 2021.

  • A. Grbac, LCD codes from two-class association schemes, Graphs and Groups, Geometries and GAP (G2G2) Summer School, Rogla, Slovenia, June 27 - July 3, 2021.

  • N. Mostarac, s-PD-sets for codes from projective planes PG(2,2h), 5 ≤ h ≤ 9, Graphs and Groups, Geometries and GAP (G2G2) Summer School, Rogla, Slovenia, June 27 - July 3, 2021.

  • A. Švob, On some periodic Golay pairs and pairwise balanced designs, 8th European Congress of Mathematics, Portorož, Slovenia, June 20 - 26, 2021.

  • T. Zrinski, Block designs constructed from orbit matrices using a modified genetic algorithm, 8th European Congress of Mathematics, Portorož, Slovenia, June 20 - 26, 2021.

  • D. Crnković, Self-orthogonal codes from block designs and association schemes, 9th Slovenian Conference on Graph Theory, Bled, Slovenia, June 23 - 29, 2019.

  • A. Švob, Self-orthogonal codes from orbit matrices of Seidel and Laplacian matrices of strongly regular graphs, 9th Slovenian Conference on Graph Theory, Bled, Slovenia, June 23 - 29, 2019.

  • T. Zrinski, Constructing block designs from orbit matrices using a modified genetic algorithm, 9th PhD Summer School in Discrete Mathematics, Rogla, Slovenia, June 30 - July 5, 2019.

  • N. Mostarac, PD-sets for codes related to flag-transitive symmetric designs, Finite Geometry & Friends (a Brussels Summer School on Finite Geometry), Brussels, Belgium, June 17 - 21, 2019.


Doktorske disertacije / PhD theses:  

  • T. Zrinski, Constructing block designs and strongly regular graphs with prescribed automorphism group using genetic algorithms, October, 2022.

  • A. Grbac, Self-dual and LCD codes from two class association schemes, November 12, 2020.


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Fakultet za matematiku Sveučilište u Rijeci