# Research

**Journal Papers:**

- N.Pace, A.Sonnino,
*"One-Factorisations of Complete Graphs Constructed in Desarguesian Planes of Certain Odd Square Orders"*, Electronic Journal of Combinatorics, Volume 27, Issue 1, January 2020 (link). - Gy.Kiss, N.Pace, A.Sonnino,
*"On circular-linear one-factorizations of the complete graph"*, Discrete Mathematics, Volume 342, Issue 12, December 2019 (link). - N.Pace, A.Sonnino,
*"One-factorisations of complete graphs arising from hyperbolae in the Desarguesian affine plane"*, Journal of Geometry, Volume 110, March 2019 (link). - N.Pace,
*"One-overlapped factorizations of non-abelian groups"*, Graphs and Combinatorics, Volume 34, Issue 6, pp 1459-1467, November 2018. (link). - G.Korchmaros, N.Pace, A.Sonnino,
*"One-factorisations of complete graphs arising from ovals in finite planes"*, Journal of Combinatorial Theory, Series A, Volume 160, pp 62-83, November 2018 (link). - N.Pace, A.Sonnino,
*"On linear codes admitting large automorphism groups"*, Designs, Codes and Cryptography, Volume 83, Issue 1, pp 115–143, April 2017 (link). - N.Pace,
*"New ternary linear codes from projectivity groups"*, Discrete Mathematics, Volume 331, pp 22-26, 28 September 2014 (link). - G.Korchmaros, G.Nagy, N.Pace,
*"k-nets embedded in a projective plane over a field"*, Combinatorica, Volume 35, Issue 1, pp 63--74, February 2015 (link). - G.Korchmaros, G.Nagy, N.Pace,
*"3-nets realizing a group in a projective plane"*, Journal of Algebraic Combinatorics, Volume 39, Issue 4, pp 939-966, June 2014 (link). - N.Pace,
*"On small complete arcs and transitive A*, J. Comb. Des., Volume 22, Issue 10, pages 425-434, October 2014 (link)._{5}-invariant arcs in the projective plane PG(2,q)" - G.Nagy, N.Pace,
*"On small 3-nets embedded in a projective plane over a field"*, Journal of Combinatorial Theory, Series A, Volume 120, Issue 7, 1632-1641, September 2013 (link). - G.Korchmaros, N.Pace,
*"Coset Intersection of Irreducible Plane Cubics"*, Designs, Codes and Cryptography, Volume 72, Issue 1, pp 53–75, July 2014 (link). - E.Kolotoglu, S.Magliveras, N.Pace,
*Related Decompositions and New Constructions of the Higman-Sims and Hall-Janko Graphs*, Australasian Journal of Combinatorics, Volume 54, October 2012 (link). - N.Pace,
*"On the distribution of the elements of a finite group generated by covers"*, Appl. Algebra Engrg. Comm. Comput., Volume 22, Numbers 5-6, 367-373, December 2011(link). - I.Ilic, S.Magliveras, N.Pace,
*"Decomposing the Higman-Sims graph into double Petersen graphs"*, J. of Combinatorial Math. and Comb. Computing (JCMCC), Volume 80, February 2012 (preprint). - G.Korchmaros, N.Pace,
*"Infinite Family of Large Complete Arcs in PG(2,q*. Designs, Codes and Cryptography, Volume 55, Numbers 2-3, May, 2010 , pp 285-296 (link).^{n}), with q odd and n>1 odd" - V.Bozovic, N.Pace,
*"Factorization of groups using free mappings"*, Journal of Algebra and its Applications, Volume: 7, Issue 5, October 2008, pp 647-662 (link)(preprint).

**Preprints:**

**Conference Presentations:**

- Combinatorics 2018, "
*On the existence of 1-overlapped factorizations of finite groups that are not cyclic or dihedral*", Arco, Italy, June 3-9, 2018. - 26th British Combinatorial Conference, "
*On the existence and construction of PD-sets for linear codes*", Glasgow, Scotland, July 3-7, 2017. - Combinatorics 2016, "
*Linear Codes, Automorphism Groups and Permutation Decoding*", Maratea, Italy, May 30-June 4, 2016. - 12th International Conference on Finite Fields and Their Applications (Fq12),
*"Code Automorphisms and Permutation Decoding of Linear Codes"*, Saratoga Springs, NY, USA, July 13-17, 2015. - XXIII Brazilian Algebra Meeting (Special Session: "Finite Fields and
Applications"),
*"Arcs and Linear Codes with Prescribed Symmetry"*, Maringá, Paraná, Brazil, July 27-August 1, 2014. - Combinatorics 2014,
*"Arcs and Linear Codes with Prescribed Automorphism Groups"*, Gaeta, Italy, June 1-6, 2014. - 45th Southeastern International Conference on Combinatorics, Graph Theory, and Computing,
Boca Raton, Florida, USA,
*"Linear Codes from Projectivity Groups "*, March 3-7, 2014. - Special Days on combinatorial constructions using finite fields, "
*k-nets in a projective plane over a field*", Special Semester on Applications of Algebra and Number Theory at RICAM, Linz, December 5, 2013. - 13th ALGA Meeting, "
*Realization of Finite Groups by 3-Nets in a Projective Plane over a Field*", Teresopolis, RJ, Brazil, June 30-July 5, 2013. - Workshop "Young Researchers in Algebra", "Complete Arcs in the Desarguesian Plane PG(2,q)", IME—USP, São Paulo, Brazil, May 24—25, 2013.
- 44th Southeastern International Conference on Combinatorics, Graph Theory, and Computing,
Boca Raton, Florida, USA,
*"On small complete arcs in projective planes"*, March 4-8, 2013. - 43rd Southeastern International Conference on Combinatorics, Graph Theory, and Computing,
Boca Raton, Florida, USA,
*"Related Decompositions of the Higman-Sims and Hall-Janko Graphs"*, March 5-9, 2012. - 2nd Istanbul Design Theory, Graph Theory and Combinatorics Conference,
*"Decomposing the Higman-Sims graph into double Petersen graphs"*, June 27-July 01, 2011. - NATO Advanced Study Institute on Information Security and Related Combinatorics, Opatija, Croatia,
*"On the Distribution of the Elements of a Finite Group Generated by Random Covers"*, May 31 - June 11 2010. - 4th Pythagorean Conference, Corfu, Greece,
*"On the distribution of elements of a finite group generated by random covers"*, May 30 - June 4 2010. - 22nd Midwest Conference on Combinatorics, Cryptography, and Computing, Las Vegas, Nevada, USA,
*"Free Mappings and Factorizations of Groups"*, October 22-24 2008.

**Seminar Presentations:**

- Algebra and Number Theory Seminar, University College Dublin,
*"Permutation decoding of linear error-correcting codes"*, April 11, 2016. - Research Seminar, School of Mathematical Sciences, Dublin Institute of Technology,
*"Finite k--nets in projective planes''*, December 11, 2015. - 1st Workshop for the ICMC/USP Postdocs,
*"Code Automorphisms and Permutation Decoding of Linear Codes from Finite Projective Geometries''*, ICMC, University of São Paulo, São Carlos, April 30, 2015. - Geometria Algébrica (p>=0) e Temas afins, IMECC, Universidade Estadual de Campinas, "Complete arcs in projective planes", April 2013.
- Algebra, Cryptography & Logic Seminar, Department of Mathematical Sciences, Florida Atlantic University,
*"3-Nets Embedded in a Projective Plane over a Field"*, Spring 2012. -
Algebra, Cryptography & Logic Seminar, Department of Mathematical Sciences, Florida Atlantic University,
*"Constructing the Desarguesian Plane PG(2,q) from PGL(2,q)"*, Fall 2010. - Crypto Meetings, Department of Mathematical Sciences, Florida Atlantic University,
*"Hyperelliptic Curves and Cryptography"*, Fall 2007.

**Scholarships/Grants:**

- Post-degree scholarship: Borsa di studio post-lauream
*“Ricerca e sviluppo di un sistema prototipale integrato HW/SW dedicato alle trasmissioni multimediali crittografate, in ambiente Internet e su linee dedicate punto-punto, basato su protocollo IPSEC ed UMTS, utilizzando come elemento crittografico un algoritmo innovativo implementato con funzioni di geometria combinatoria”*, April-June 2006. Department of Mathematics and Computer Science. Università degli Studi della Basilicata (Italy). (link)