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), email: 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 selforthogonal codes, Util. Math. 109 (2018),
227253.

D. Crnković, R. Egan, A note on Siamese twin designs intersecting in a
BIBD and a PBD, Math. Comput. Sci. 12 (2018), 389395.

D. Dumičić Danilović, On some new resolvable 1rotational (45,5,2)BIBDs,
Bull. Inst. Combin. Appl. 84 (2018), 5364.

D. Crnković, N. Mostarac, Selfdual codes from orbit matrices and quotient
matrices of combinatorial designs, Discrete Math. 341 (2018),
33313343.

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), 2338.

D. Crnković, V. Mikulić Crnković, B. G. Rodrigues, On selforthogonal
designs and codes related to Held's simple group, Adv. Math. Commun. 12
(2018), 607628.

D. Crnković, S. Rukavina, A. Švob, New strongly regular graphs from
orthogonal groups $O^+(6,2)$ and $O^(6,2)$, Discrete Math. 341 (2018),
27232728.

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), 11991209.

D. Crnković, N. Mostarac, PDsets for codes related to flagtransitive
symmetric designs, Trans. Comb. 7 (2018), 3750.

D. Crnković, Regular Hadamard matrices constructed from Hadamard 2designs
and conference graphs, Discrete Math. 341 (2018), 520524.

R. Egan, On equivalence of negaperiodic Golay pairs, Des. Codes Cryptogr.
85 (2017), 523532.

D. Crnković, V. Mikulić Crnković, A. Švob, New 3designs and 2designs
having U(3,3) as an automorphism group, Discrete Math. 340 (2017),
25072515.

D. Crnković, B. G. Rodrigues, S. Rukavina, V. D. Tonchev, Quasisymmetric
2(64,24,46) designs derived from AG(3,4), Discrete Math. 340 (2017),
24722478.

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), 2340.

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), 145154.

D. Crnković, M. Maksimović, B. G. Rodrigues, S. Rukavina, Selforthogonal
codes from the strongly regular graphs on up to 40 vertices, Adv. Math.
Commun. 10 (2016), 555582.

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), 119138.

D. Crnković, S. Rukavina, Selfdual codes from extended orbit matrices of
symmetric designs, Des. Codes Cryptogr. 79 (2016), 113120.

D. Crnković, N. Mostarac, S. Rukavina, Selfdual codes from quotient
matrices of symmetric divisible designs with the dual property, Discrete
Math. 339 (2016), 409414.

M. De Boeck, L. Storme, A. Švob, The CameronLiebler problem for
sets, Discrete Math. 339 (2016), 470474.

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, 4360.

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, 6169.

D. Crnković, W. H. Haemers, Walkregular divisible design graphs, Des.
Codes Cryptogr. 72 (2014), 165175.

D. Crnković, Classes of selforthogonal or selfdual codes from orbit
matrices of Menon designs, Discrete Math. 327 (2014), 9195.

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), 1940

D. Crnković, D. Dumičić Danilović, Finding unitals in symmetric designs using a modified genetic algorithm, Math. Pannon. 24 (2013), 183196.
Pozvana predavanja:

S. Rukavina, Construction of selforthogonal linear codes from orbit
matrices of combinatorial structures, 8th PhD Summer School in Discrete
Mathematics, Rogla, Slovenia, July 17, 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 1014,
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 2630, 2015.

S. Rukavina, Codes from orbit matrices of symmetric designs, Algebraic
Combinatorics and Applications  The first annual Kliakhandler Conference,
Houghton, USA, August 2630, 2015.

D. Crnković, Transitive designs constructed from finite groups and related
codes, CIMPA Research School Algebraic Representation Theory 2015, Cape
Town, South Africa, July 1931, 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 17, 2018.

M. Mravić, Binary Codes from Skewsymmetric Hadamard Matrices, 8th PhD
Summer School in Discrete Mathematics, Rogla, Slovenia, July 17, 2018.

D. Crnković, On some regular Hadamard matrices and associated codes,
Combinatorics 2018, Arco, Italy, June 39, 2018.

S. Rukavina, Codes from orbit matrices of strongly regular graphs,
Combinatorics 2018, Arco, Italy, June 39, 2018.

A. Švob, Orbit matrices of Hadamard matrices and related codes,
Combinatorics 2018, Arco, Italy, June 39, 2018.

R. Egan, Morphisms of Butson matrices, Combinatorics 2018, Arco, Italy,
June 39, 2018.

D. Crnković, Strongly regular graphs constructed from groups, Symmetry vs
Regularity, Pilsen, Czech Republic, July 17, 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 17, 2018.

N. Mostarac, Selfdual 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, Selforthogonal 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 12, 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 49, 2017.

A. Švob, tdesigns and strongly regular graphs constructed from some
linear groups, Colloquium on Combinatorics, Paderborn, Germany, November
2425, 2017.

M. Šimac, LDPC codes constructed from Moore graphs with diameter 2,
Colloquium on Combinatorics, Paderborn, Germany, November 2425, 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 1014, 2017

D. Crnković, A construction of regular Hadamard matrices, The Second Malta
Conference in Graph Theory and Combinatorics, Qawra, Malta, June 2630,
2017

S. Rukavina, Quasisymmetric 2(64,24,46) designs derived from AG(3,4),
The Second Malta Conference in Graph Theory and Combinatorics, Qawra,
Malta, June 2630, 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 2124, 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 2124, 2017

V. Mikulić Crnković, On a method of constructing geometric designs, Hypergraphs, Graphs and Designs, Sant'Alessio Siculo, Italy, June 2124, 2017

A. Švob, Construction of designs from the unitary group U(3,3), Workshop on permutation groups: methods and applications, Bielefeld, Germany, January 1214, 2017 (poster)

V. Mikulić Crnković, Selforthogonal designs and codes from Held's group, Workshop on permutation groups: methods and applications, Bielefeld, Germany, January 1214, 2017 (poster)

D. Dumičić Danilović, Application of a genetic algorithm on block designs, Colloquium on Combinatorics, Paderborn, Germany, November 45, 2016

M. Maksimović, Construction of codes from orbit matrices of strongly regular graphs, Colloquium on Combinatorics, Paderborn, Germany, November 45, 2016

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

D. Dumičić Danilović, On construction of 2designs and related selforthogonal codes, 6th Croatian Mathematical Congress, Zagreb, Croatia, June 1417, 2016

M. Maksimović, Form orbit matrices to strongly regular graphs and codes, 6th Croatian Mathematical Congress, Zagreb, Croatia, June 1417, 2016

V. Mikulić Crnković, On some codes invariant under the action of the Held group, 6th Croatian Mathematical Congress, Zagreb, Croatia, June 1417, 2016

D. Crnković, Regular Hadamard matrices, 12th Nordic
Combinatorial Conference (NORCOM), Levi, Kittilä, Finland, June 1315, 2016

S. Rukavina, Selfdual codes from quotient matrices of symmetric divisible designs with
the dual property, 12th Nordic
Combinatorial Conference (NORCOM), Levi, Kittilä, Finland, June 1315, 2016

D. Dumičić Danilović, Block designs and selforthogonal codes constructed from orbit matrices, Network Coding and Designs, Dubrovnik, Croatia, April 48, 2016

V. Mikulić Crnković, On selforthogonal codes generated by orbit matrices of 1designs, Network Coding and Designs, Dubrovnik, Croatia, April 48, 2016

M. Šimac, LDPC codes based on μgeodetic graphs, Network Coding and Designs, Dubrovnik, Croatia, April 48, 2016

A. Švob, The CameronLiebler problem for sets, Network Coding and Designs, Dubrovnik, Croatia, April 48, 2016

D. Crnković, Groups acting on combinatorial designs and related codes,
Symmetries and Covers of Discrete Objects, Queenstown, New Zealand,
1419 February 2016

S. Rukavina, Orbit matrices of symmetric designs and related selfdual codes, Symmetries and Covers of Discrete Objects, Queenstown, New Zealand, 1419 February 2016

V. Mikulić Crnković, On selforthogonal binary codes invariant under the action of the Held group, Design and Application of Random Network Codes,
Istanbul, Turkey, November 46, 2015.

A. Švob, Designs on which the unitary group U(3,3) acts transitively, Design and Application of Random Network Codes,
Istanbul, Turkey, November 46, 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, Selfdual 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 nontransitive graphs from groups, 8th Slovenian Conference on Graph Theory, Kranjska Gora, Slovenia, June 21  27, 2015

S. Rukavina, Some properties of kgeodetic 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, Selfdual 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, Selforthogonal or selfdual 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 kgeodetic 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 PDskupovi 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.
