Potpore istraživanja Sveučilišta u Rijeci

 

Blok dizajni, jako regularni grafovi i srodne kombinatoričke strukture

Odjel za matematiku Sveučilišta u Rijeci

 

 

Odjel za matematiku

Sveučilište u Rijeci

 

 

U sklopu projekta istraživat će se kombinatorički dizajni, razni tipovi grafova (posebno jako regularni grafovi) i kodovi, i veza između tih struktura. Uz linearne kodove nad poljima proučavat će se i kodovi nad prstenima i kvantni kodovi. Za konstrukciju navedenih struktura koristit će se algebarske strukture kao što su konačne grupe, konačna polja i vektorski prostori, te računalni programi. Za konstrukciju blok dizajna uglavnom će se koristiti konstrukcija iz konačnih grupa i konstrukcija pomoću orbitnih matrica. Iz konstruiranih kombinatoričkih struktura konstruirat će se kodovi. Također će se proučavati i kombinatoričke strukture dobivene iz kodova. Proučavat će se geometrijska svojstva konstruiranih struktura kao i njihove grupe autormorfizama. Konstruirane strukture usporedit će se s poznatim strukturama. Kao rezultat istraživanja očekuje se konstrukcija kodova s dobrim svojstvima, po mogućnosti boljim svojstvima od do sada poznatih kodova, i konstrukcija i klasifikacija raznih kombinatoričkih struktura.

 

Voditelj:

prof. dr. sc. Dean Crnković (Odjel za matematiku Sveučilišta u Rijeci), e-mail: deanc@math.uniri.hr

Istraživački tim:

prof. dr. sc. Dean Crnković (Odjel za matematiku Sveučilišta u Rijeci)

dr. sc. Doris Dumičić Danilović (Odjel za matematiku Sveučilišta u Rijeci)

Ana Grbac (Odjel za matematiku Sveučilišta u Rijeci)

dr. sc. Marija Maksimović (Odjel za matematiku Sveučilišta u Rijeci)

doc. dr. sc. Vedrana Mikulić Crnković (Odjel za matematiku Sveučilišta u Rijeci)

Nina Mostarac (Odjel za matematiku Sveučilišta u Rijeci)

prof. dr. sc. Sanja Rukavina (Odjel za matematiku Sveučilišta u Rijeci)

dr. sc. Loredana Simčić (Tehnički fakultet u Rijeci)

dr. sc. Marina Šimac (Odjel za matematiku Sveučilišta u Rijeci)

dr. sc. Andrea Švob (Odjel za matematiku Sveučilišta u Rijeci)

Sanja Vranić

 

Objavljeni radovi:

  • D. Crnković, D. Dumičić Danilović, S. Rukavina, Enumeration of symmetric (45,12,3) designs with nontrivial automorphisms, J. Algebra Comb. Discrete Struct. Appl. 3 (2016), 145-154.

  • D. Crnković, M. Maksimović, B. G. Rodrigues, S. Rukavina, Self-orthogonal codes from the strongly regular graphs on up to 40 vertices, Adv. Math. Commun. 10 (2016), 555-582.

  • D. Crnković, V. Mikulić Crnković, A. Švob, On some transitive combinatorial structures and codes constructed from the symplectic group S(6,2), J. Combin. Math. Combin. Comput. 97 (2016), 119-138.

  • D. Crnković, S. Rukavina, Self-dual codes from extended orbit matrices of symmetric designs, Des. Codes Cryptogr. 79 (2016), 113-120.

  • D. Crnković, N. Mostarac, S. Rukavina, Self-dual codes from quotient matrices of symmetric divisible designs with the dual property, Discrete Math. 339 (2016), 409-414.

  • M. De Boeck, L. Storme, A. Švob, The Cameron-Liebler problem for sets, Discrete Math. 339 (2016), 470-474.

  • D. Crnković, H. Kharaghani, Divisible design digraphs, in: Algebraic Design Theory and Hadamard Matrices, (C. J. Colbourn, Ed.), Springer Proc. Math. Stat., Vol. 133, Springer, New York, 2015, 43-60.

  • D. Crnković, S. Rukavina, V. D. Tonchev, New symmetric (61,16,4) designs obtained from codes, in: Algebraic Design Theory and Hadamard Matrices, (C. J. Colbourn, Ed.), Springer Proc. Math. Stat., Vol. 133, Springer, New York, 2015, 61-69.

  • D. Crnković, W. H. Haemers, Walk-regular divisible design graphs, Des. Codes Cryptogr. 72 (2014), 165-175.

  • D. Crnković, Classes of self-orthogonal or self-dual codes from orbit matrices of Menon designs, Discrete Math. 327 (2014), 91-95.

  • D. Crnković, V. Mikulić Crnković, A. Švob, On some transitive combinatorial structures constructed from the unitary group U(3,3), J. Statist. Plann. Inference 144 (2014), 19-40

  • D. Crnković, D. Dumičić Danilović, Finding unitals in symmetric designs using a modified genetic algorithm, Math. Pannon. 24 (2013), 183-196.

 

Pozvana predavanja:  

  • D. Crnković, Block designs constructed from groups, 2016 PhD Summer School in Discrete Mathematics, Rogla, Slovenia, June 26 - July 2, 2016

  • D. Crnković, Incidence structures from groups and related codes, Algebraic Combinatorics and Applications - The first annual Kliakhandler Conference, Houghton, USA, August 26-30, 2015.

  • S. Rukavina, Codes from orbit matrices of symmetric designs, Algebraic Combinatorics and Applications - The first annual Kliakhandler Conference, Houghton, USA, August 26-30, 2015.

  • D. Crnković, Transitive designs constructed from finite groups and related codes, CIMPA Research School Algebraic Representation Theory 2015, Cape Town, South Africa, July 19-31, 2015.

  • D. Crnković, On some codes and divisible designs constructed from Hadamard matrices, Workshop on Algebraic Design Theory and Hadamard Matrices 2014, Lethbridge, Kanada, 8. - 11. srpnja 2014.

 

Izlaganja na konferencijama:  

  • A. Švob, Construction of designs from the unitary group U(3,3), Workshop on permutation groups: methods and applications, Bielefeld, Germany, January 12-14, 2017 (poster)

  • V. Mikulić Crnković, Self-orthogonal designs and codes from Held's group, Workshop on permutation groups: methods and applications, Bielefeld, Germany, January 12-14, 2017 (poster)

  • D. Dumičić Danilović, Application of a genetic algorithm on block designs, Colloquium on Combinatorics, Paderborn, Germany, November 4-5, 2016

  • M. Maksimović, Construction of codes from orbit matrices of strongly regular graphs, Colloquium on Combinatorics, Paderborn, Germany, November 4-5, 2016

  • M. Šimac, Absorbing sets in the Tanner graphs of LDPC codes derived from μ-geodetic graphs, 2016 PhD Summer School in Discrete Mathematics, Rogla, Slovenia, June 26 - July 2, 2016

  • D. Dumičić Danilović, On construction of 2-designs and related self-orthogonal codes, 6th Croatian Mathematical Congress, Zagreb, Croatia, June 14-17, 2016

  • M. Maksimović, Form orbit matrices to strongly regular graphs and codes, 6th Croatian Mathematical Congress, Zagreb, Croatia, June 14-17, 2016

  • V. Mikulić Crnković, On some codes invariant under the action of the Held group, 6th Croatian Mathematical Congress, Zagreb, Croatia, June 14-17, 2016

  • D. Crnković, Regular Hadamard matrices, 12th Nordic Combinatorial Conference (NORCOM), Levi, Kittilä, Finland, June 13-15, 2016

  • S. Rukavina, Self-dual codes from quotient matrices of symmetric divisible designs with the dual property, 12th Nordic Combinatorial Conference (NORCOM), Levi, Kittilä, Finland, June 13-15, 2016

  • D. Dumičić Danilović, Block designs and self-orthogonal codes constructed from orbit matrices, Network Coding and Designs, Dubrovnik, Croatia, April 4-8, 2016

  • V. Mikulić Crnković, On self-orthogonal codes generated by orbit matrices of 1-designs, Network Coding and Designs, Dubrovnik, Croatia, April 4-8, 2016

  • M. Šimac, LDPC codes based on μ-geodetic graphs, Network Coding and Designs, Dubrovnik, Croatia, April 4-8, 2016

  • A. Švob, The Cameron-Liebler problem for sets, Network Coding and Designs, Dubrovnik, Croatia, April 4-8, 2016

  • D. Crnković, Groups acting on combinatorial designs and related codes, Symmetries and Covers of Discrete Objects, Queenstown, New Zealand, 14-19 February 2016

  • S. Rukavina, Orbit matrices of symmetric designs and related self-dual codes, Symmetries and Covers of Discrete Objects, Queenstown, New Zealand, 14-19 February 2016

  • V. Mikulić Crnković, On self-orthogonal binary codes invariant under the action of the Held group, Design and Application of Random Network Codes, Istanbul, Turkey, November 4-6, 2015.

  • A. Švob, Designs on which the unitary group U(3,3) acts transitively, Design and Application of Random Network Codes, Istanbul, Turkey, November 4-6, 2015.

  • D. Dumičić Danilović, Construction of block designs admitting a solvable automorphism group, PhD Summer School in Discrete Mathematics, Rogla, Slovenia, June 27 - July 3, 2015

  • M. Maksimović, Orbit matrices of strongly regular graphs, PhD Summer School in Discrete Mathematics, Rogla, Slovenia, June 27 - July 3, 2015

  • N. Mostarac, Self-dual codes from quotient matrices of symmetric divisible designs with the dual property, PhD Summer School in Discrete Mathematics, Rogla, Slovenia, June 27 - July 3, 2015

  • M. Šimac, LDPC codes based on $\mu$-geodetic graphs obtained from block designs, PhD Summer School in Discrete Mathematics, Rogla, Slovenia, June 27 - July 3, 2015

  • V. Mikulić Crnković, On the construction of non-transitive graphs from groups, 8th Slovenian Conference on Graph Theory, Kranjska Gora, Slovenia, June 21 - 27, 2015

  • S. Rukavina, Some properties of k-geodetic graphs, 8th Slovenian Conference on Graph Theory, Kranjska Gora, Slovenia, June 21 - 27, 2015

  • D. Crnković, On some Menon designs and related structures, ALCOMA15, Kloster Banz, Njemačka, 15.-20. ožujka, 2015.

  • D. Dumičić Danilović, Construction of block designs admitting a solvable automorphism group, ALCOMA15, Kloster Banz, Njemačka, 15.-20. ožujka, 2015.

  • S. Rukavina, Self-dual codes from extended orbit matrices of symmetric designs, ALCOMA15, Kloster Banz, Njemačka, 15.-20. ožujka, 2015.

  • A. Švob, Transitive combinatorial structures invariant under some subgroups of S(6,2), ALCOMA15, Kolster Banz, Njemačka, 15.-20. ožujka, 2015.

  • D. Crnković, Self-orthogonal or self-dual codes from orbit matrices of block designs, Mathematics of Communications: Sequences, Codes and Designs, Banff, Kanada, 25.-30. siječnja 2015.

  • A. Švob, On some transitive combinatorial structures and codes constructed from the symplectic group S(6,2), Colloquium on finite geometry, coding theory and cryptography, Gent, Belgija, 7. studeni 2014

  • S. Rukavina, On k-geodetic graphs from symmetric (71,15,3) designs and their residual and derived designs, Combinatorics 2014, Gaeta, Italija, 1.-6. lipnja 2014.

  • L. Simčić, Codes constructed from orbit matrices of block designs, Symmetries of Graphs and Networks IV and 2014 PhD Summer School in Discrete Mathematics, Rogla, Slovenija, 29. lipnja - 5. srpanja 2014.

  • A. Švob, Transitive combinatorial structures constructed from finite groups, Symmetries of Graphs and Networks IV and 2014 PhD Summer School in Discrete Mathematics, Rogla, Slovenija, 29. lipnja - 5. srpanja 2014

 

Doktorske disertacije:  

  • Marina Šimac, LDPC kodovi konstruirani iz nekih kombinatoričkih struktura, 23. ožujka 2017. godine

  • Marija Maksimović, Orbitne matrice jako regulranih grafova, 23. ožujka 2015. godine

  • Doris Dumičić Danilović, Poopćenje i profinjenje nekih algoritama za konstrukciju blokovnih dizajna i istraživanje njihovih podstruktura, 20. studeni 2014. godine

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

 

Odjel za matematiku Sveučilište u Rijeci