HRZZ Research Project

Galois geometry and coherent configurations

GalGeKo - 5713

1/1/2021 - 31/12/2025

University of Rijeka, Faculty of Mathematics

 

 
 

 

The main objective of this project is to make significant contributions to several different areas of mathematics in the field of discrete and combinatorial mathematics, especially to the studies of Galois geometry and coherent configurations and finite incidence structures connected with them. We will focus on developing methods of construction of combinatorial structures that are relying on Galois geometry and coherent configurations. We will construct, analyse and describe structures obtained from finite groups, especially geometrical groups for which deep study in Galois geometry is crucial. We will try to establish new perspective group and make invaluable results in the mentioned fields using new modern approach to the study of these structures especially in the area of Galois geometry that discrete structures are part of. The project will mostly deal with the interplay between Galois geometry and combinatorial structures and their connection to coherent configurations.

 

Principal Investigator:

Andrea Švob (University of Rijeka, Faculty of Mathematics), e-mail: asvob@math.uniri.hr

 

Associates:

Maarten De Boeck (University of Rijeka, Faculty of Mathematics)

Ana Grbac (University of Rijeka, Faculty of Mathematics)

Nina Mostarac (University of Rijeka, Faculty of Mathematics)

Tin Zrinski (University of Rijeka, Faculty of Mathematics)

 

 

Papers:

  • D. Crnković, A. Švob, New example of strongly regular graph with parameters (81,30,9,12) and a simple group A5 as the automorphism group, Examples and Counterexamples, to appear.

  • D. Crnković, A. Švob, Constructing doubly even self-dual codes and even unimodular lattices from Hadamard matrices, Appl. Algebra Engrg. Comm. Comput., to appear.

  • D. Crnković, A. Švob, LCD subspace codes, Des. Codes Cryptogr., to appear.

  • D. Crnković, A. Švob, Tolerance fuzzy graphs, J. Intell. Fuzzy Systems, to appear.

  • S. Adriaensen, M. De Boeck, L. Denaux, Blocking subspaces with points and hyperplanes, Australas. J. Combin. 85 (2023), 340–349.

  • D. Crnković, H. Kharaghani, S. Suda, A. Švob, New constructions of Deza digraphs, Int. J. Group Theory (2023), to appear.

  • D. Crnković, A. Grbac, A. Švob, Block designs from self-dual codes obtained from Paley designs and Paley graphs, Glas. Mat. Ser. III (2023), to appear.

  • M. De Boeck, G. Van De Voorde, Embedded antipodal planes and the minimum weight of the dual code of points and lines in projective planes of order p2, Des. Codes Cryptogr. (2022), to appear.

  • D. Crnković, V. Mikulić Crnković, F. Pavese, A. Švob, Construction of the projective plane PG(2,q2) from the unitary group PSU(3,q), Contrib. Discrete Math. (2022), to appear.

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

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

  • A. Švob, LCD codes from equitable partitions of association schemes, Appl. Algebra Engrg. Comm. Comput., to appear.

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

 

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.

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

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

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

  • M. De Boeck, Cameron-Liebler sets for hyperbolic quadrics, Combinatorial Constructions Workshop, Zagreb, Croatia, June 27-29, 2022.

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

  • M. De Boeck, The weight distributions of linear sets in PG(1,q^5), Combinatorics 2022, Mantua, Italy, May 30 - June 3, 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.

  • 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.

  • A. Grbac, On some constructions of LCD codes, 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.

  • 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.

 

PhD theses:

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

 

Meetings:

  • Rijeka Conference on Combinatorial Objects and Their Applications (RICCOTA2023), July 3 – 7, 2023.