HRZZ Research Project

Combinatorial Objects and Codes

(2019-2022)

University of Rijeka, Department of Mathematics

 

 

Outcomes

 

 

This project deals with construction and analysis of various types of combinatorial designs and graphs. 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. Further, we will work on construction and analysis of codes, mostly linear codes that can be obtained from combinatorial designs, graphs, binary sequences and Hadamard matrices. 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-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.

 

Principal Investigator:

Dean Crnković (University of Rijeka, Department of Mathematics), e-mail: deanc@math.uniri.hr

 

Associates

Sara Ban (University of Rijeka, Department of Mathematics)

Doris Dumičić Danilović (University of Rijeka, Department of Mathematics)

Vedran Krčadinac (University of Zagreb, Faculty of Science)

Marija Maksimović (University of Rijeka, Department of Mathematics)

Vedrana Mikulić Crnković (University of Rijeka, Department of Mathematics)

Nina Mostarac (University of Rijeka, Department of Mathematics)

Matteo Mravić (University of Rijeka, Department of Mathematics)

Anamari Nakić (University of Zagreb, Faculty of Electrical Engineering and Computing)

Ivona Novak (University of Rijeka, Department of Mathematics)

Mario Pavčević (University of Zagreb, Faculty of Electrical Engineering and Computing)

Sanja Rukavina (University of Rijeka, Department of Mathematics)

Marina Šimac (University of Rijeka, Department of Mathematics)

Andrea Švob (University of Rijeka, Department of Mathematics)

Kristijan Tabak (Rochester Institute of Technology Croatia)

Renata Vlahović (University of Zagreb, Faculty of Science)

Tin Zrinski (University of Rijeka, Department of Mathematics)