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:

Sara Ban (Odjel za matematiku Sveučilišta u Rijeci)

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)

dr. sc. Nina Mostarac (Odjel za matematiku Sveučilišta u Rijeci)

Matteo Mravić (Odjel za matematiku Sveučilišta u Rijeci)

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

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

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

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

Sanja Vranić

 

Objavljeni radovi:

  • D. Crnković, D. Dumičić Danilović, S. Rukavina, On symmetric (78,22,6) designs and related self-orthogonal codes, Util. Math. 109 (2018), 227-253.

  • D. Crnković, R. Egan, A note on Siamese twin designs intersecting in a BIBD and a PBD, Math. Comput. Sci. 12 (2018), 389-395.

  • D. Dumičić Danilović, On some new resolvable 1-rotational (45,5,2)-BIBDs, Bull. Inst. Combin. Appl. 84 (2018), 53-64.

  • D. Crnković, N. Mostarac, Self-dual codes from orbit matrices and quotient matrices of combinatorial designs, Discrete Math. 341 (2018), 3331-3343.

  • D. Crnković, V. Mikulić Crnković, A. Švob, Transitive combinatorial structures invariant under some subgroups of S(6,2) and related codes, Atti Accad. Peloritana Pericolanti Cl. Sci. Fis. Mat. Natur. 96, No. S2, A6 (2018), 15 pages.

  • D. Crnković, M. Maksimović, S. Rukavina, Codes from orbit matrices of strongly regular graphs, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 22(536) (2018), 23-38.

  • D. Crnković, V. Mikulić Crnković, B. G. Rodrigues, On self-orthogonal designs and codes related to Held's simple group, Adv. Math. Commun. 12 (2018), 607-628.

  • D. Crnković, S. Rukavina, A. Švob, New strongly regular graphs from orthogonal groups $O^+(6,2)$ and $O^-(6,2)$, Discrete Math. 341 (2018), 2723-2728.

  • M. Maksimović, Enumeration of Strongly Regular Graphs on up to 50 Vertices Having S_3 as an Automorphism Group, Symmetry 10(6), 212 (2018).

  • D. Crnković, R. Egan, A. Švob, Orbit matrices of Hadamard matrices and related codes, Discrete Math. 341 (2018), 1199-1209.

  • D. Crnković, N. Mostarac, PD-sets for codes related to flag-transitive symmetric designs, Trans. Comb. 7 (2018), 37-50.

  • D. Crnković, Regular Hadamard matrices constructed from Hadamard 2-designs and conference graphs, Discrete Math. 341 (2018), 520-524.

  • R. Egan, On equivalence of negaperiodic Golay pairs, Des. Codes Cryptogr. 85 (2017), 523-532.

  • D. Crnković, V. Mikulić Crnković, A. Švob, New 3-designs and 2-designs having U(3,3) as an automorphism group, Discrete Math. 340 (2017), 2507-2515.

  • D. Crnković, B. G. Rodrigues, S. Rukavina, V. D. Tonchev, Quasi-symmetric 2-(64,24,46) designs derived from AG(3,4), Discrete Math. 340 (2017), 2472-2478.

  • D. Crnković, S. Rukavina, L. Simčić, On triplanes of order twelve admitting an automorphism of order six and their binary and ternary codes, Util. Math. 103 (2017), 23-40.

  • 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:  

  • S. Rukavina, Construction of self-orthogonal linear codes from orbit matrices of combinatorial structures, 8th PhD Summer School in Discrete Mathematics, Rogla, Slovenia, July 1-7, 2018.

  • D. Crnković, A construction of regular Hadamard matrices and related codes, 5th Workshop on Real and Complex Hadamard Matrices and Applications, Budapest, Hungary, July 10-14, 2017.

  • 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:  

  • S. Ban, Extremal Type II $Z_4$-codes from some 2-(31,15,7) designs, 8th PhD Summer School in Discrete Mathematics, Rogla, Slovenia, July 1-7, 2018.

  • M. Mravić, Binary Codes from Skew-symmetric Hadamard Matrices, 8th PhD Summer School in Discrete Mathematics, Rogla, Slovenia, July 1-7, 2018.

  • D. Crnković, On some regular Hadamard matrices and associated codes, Combinatorics 2018, Arco, Italy, June 3-9, 2018.

  • S. Rukavina, Codes from orbit matrices of strongly regular graphs, Combinatorics 2018, Arco, Italy, June 3-9, 2018.

  • A. Švob, Orbit matrices of Hadamard matrices and related codes, Combinatorics 2018, Arco, Italy, June 3-9, 2018.

  • R. Egan, Morphisms of Butson matrices, Combinatorics 2018, Arco, Italy, June 3-9, 2018.

  • D. Crnković, Strongly regular graphs constructed from groups, Symmetry vs Regularity, Pilsen, Czech Republic, July 1-7, 2018.

  • S. Rukavina, The construction of combinatorial structures and linear codes from orbit matrices of strongly regular graphs, Symmetry vs Regularity, Pilsen, Czech Republic, July 1-7, 2018.

  • N. Mostarac, Self-dual codes from orbit matrices and quotient matrices of combinatorial designs, Graphs, groups, and more: celebrating Brian Alspach's 80th and Dragan Marušič's 65th birthdays,Koper, Slovenia, May 28 - June 1, 2018.

  • M. Maksimović, Self-orthogonal codes from orbit matrices of strongly regular graphs, Graphs, groups, and more: celebrating Brian Alspach's 80th and Dragan Marušič's 65th birthdays,Koper, Slovenia, May 28 - June 1, 2018.

  • A. Švob, Strongly regular graphs and groups, Discretaly: A Workshop in Discrete Mathematics, Rome, Italy, February 1-2, 2018.

  • V. Mikulić Crnković, On combinatorial structures constructed from unitary groups U(3,q), q= 3,4,5,7, 5th International Combinatorics Conference (5ICC), Melbourne, Australia, December 4-9, 2017.

  • A. Švob, t-designs and strongly regular graphs constructed from some linear groups, Colloquium on Combinatorics, Paderborn, Germany, November 24-25, 2017.

  • M. Šimac, LDPC codes constructed from Moore graphs with diameter 2, Colloquium on Combinatorics, Paderborn, Germany, November 24-25, 2017.

  • 4. R. Egan, Phased unitary Golay pairs and Butson Hadamard matrices, All Kinds of Mathematics Remind me of You - Conference to celebrate the 70th Anniversary of Peter J. Cameron, Lisabon, Portugal, July 28, 2017

  • R. Egan, Phased unitaries and a conjecture of Ito’s, 5th Workshop on Real and Complex Hadamard Matrices and Applications, Budapest, Hungary, July 10-14, 2017

  • D. Crnković, A construction of regular Hadamard matrices, The Second Malta Conference in Graph Theory and Combinatorics, Qawra, Malta, June 26-30, 2017

  • S. Rukavina, Quasi-symmetric 2-(64,24,46) designs derived from AG(3,4), The Second Malta Conference in Graph Theory and Combinatorics, Qawra, Malta, June 26-30, 2017

  • S. Rukavina, The construction of combinatorial structures and linear codes from orbit matrices of strongly regular graphs, Hypergraphs, Graphs and Designs, Sant'Alessio Siculo, Italy, June 21-24, 2017

  • A. Švob, New strongly regular graphs from orthogonal groups $O^+(6,2)$ and $O^-(6,2)$, Hypergraphs, Graphs and Designs, Sant'Alessio Siculo, Italy, June 21-24, 2017

  • V. Mikulić Crnković, On a method of constructing geometric designs, Hypergraphs, Graphs and Designs, Sant'Alessio Siculo, Italy, June 21-24, 2017

  • 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:  

  • Nina Mostarac, Samodualni kodovi i PD-skupovi konstruirani iz kombinatoričkih dizajna, 25. listopada 2017. godine

  • 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