My research is focussed on the areas of combinatorics, algebra, Galois geometry, finite geometry, incidence geometry, finite fields and coding theory. More specifically, arcs in projective spaces, finite semifields (non-associative division algebras), projective planes, Segre varieties, Veronese varieties, geometry of tensor product spaces, translation generalised quadrangles (equivalent to the theory of eggs in projective spaces), polynomial techniques in finite geometry, field reduction techniques, linear sets, MDS codes, MRD codes, and the links between incidence geometry and coding theory.
Check out our FinInG package for computation in Finite Incidence Geometry.
Tensors in Finite Geometry (18 November 2020, Seminars and e-Seminars Arbeitsgemeinschaft in Codierungstheorie und Kryptographie, Mathematics Institute, University of Zurich, Switzerland)
(video)
Preprints are available on arXiv.org for most of my published research articles. These preprints may differ from the published version (for which I have signed a copyright agreement). In case you want a reprint of a published article (e.g. for references), you can download the publication from the journal website, or contact me.
On the geometry of the Hermitian Veronese curve and its quasi-Hermitian surfaces (with M. Lia and F. Pavese) (preprint. Discrete Mathematics (2023).
A classification of planes intersecting the Veronese surface over finite fields of even order (with N. Alnajjarine) preprint. Designs Codes and Cryptography (2023).
Waring identifiable subspaces over finite fields (with F. Zullo)
preprint.
Symplectic 4-dimensional semifields of order \(8^4\) and \(9^4\) (with J. Sheekey)
preprint. Designs Codes and Cryptography (2023).
Solids in the space of the Veronese surface in even characteristic (with N. Alnajjarine and T. Popiel)
preprint. Finite Fields and Their Applications (2022).
The tensor rank of semifields of order 16 and 81 (with J. Sheekey)
preprint. Linear Algebra and Its Applications (2022).
On pencils of cubics on the projective line over finite fields of characteristic \(>3\) (with G. Günay)
preprint. Finite Fields and Their Applications (2022).
Locally repairable codes with high availability based on generalised quadrangles (with G. Van de Voorde)
preprint.
Advances in Mathematics of Communications (2022)
On additive MDS codes over small fields (with S. Ball and G. Gamboa)
preprint. Advances in Mathematics of Communications (2023).
Combinatorial invariants for nets of conics in \({\mathrm{PG}}(2,q)\) (with T. Popiel and J. Sheekey)
preprint. Designs Codes and Cryptography (2021).
On planar arcs of size \((q+3)/2\) (with G. Günay))
preprint. Journal of Combinatorial Designs (2021).
Nets of conics of rank one in \({\mathrm{PG}}(2,q)\), \(q\) odd (with T. Popiel and J. Sheekey)
preprint. Journal of Geometry (2020)
Determining the rank of tensors in \({\mathbb{F}}_q^2\otimes {\mathbb{F}}_q^3\otimes{\mathbb{F}}_q^3\) (with N. Alnajjarine). Springer's Lecture Notes in Computer Science (LNCS) (2020) preprint. The paper has an accompanying webpage containing GAP code to determine the orbit of tensors in this 18-dimensional vector space.
Arcs and tensors (with S. Ball) preprint. Des. Codes Cryptogr. (2020)
The symmetric representation of lines in PG\((F^3\otimes F^3)\) (with T. Popiel) preprint. Discrete Mathematics (2020)
Arcs in finite projective spaces (with S. Ball)
preprint. EMS Surveys of Mathematical Sciences (2019)
Classification of 8-dimensional rank two commutative semifields (with M. Rodgers) preprint. Advances in Geometry (2019)
Planar arcs (with S. Ball) preprint. Journal of Combinatorial Theory. Series A. (2018)
The BEL-rank of finite semifields (with J. Sheekey)
preprint. Des. Codes Cryptogr. (2017)
Classification of subspaces in \(F^2 \otimes F^3\) and orbits in \(F^2\otimes F^3 \otimes F^r\) (with J. Sheekey)
preprint. Journal of Geometry (2017)
Scattered Spaces in Galois Geometry
preprint. Article in Contemporary Developments in Finite Fields and Applications (2016)
Canonical forms of 2x3x3 tensors over the real field,
algebraically closed fields, and finite fields (with J. Sheekey)
preprint. Linear Algebra and its Applications (2015)
Subspaces intersecting each element of a regulus in one point, André-Bruck-Bose representation and clubs (with C. Zanella)
preprint. Electronic Journal of Combinatorics (2016)
On BEL-configurations and finite semifields (with J. Sheekey). Des. Codes Cryptogr. preprint. Designs Codes and Cryptography (2016)
Subgeometries and linear sets on a projective line (with C. Zanella). preprint. Finite Fields Appl. (2015)
Field reduction and linear sets in finite geometry (with G. Van de Voorde). Topics in Finite Fields, AMS Contemporary Math. Edited by G. Kyureghyan, G. L. Mullen, and A. Pott (2015) preprint.
The isotopism problem of a class of 6-dimensional rank 2 semifields and its solution (with G. Marino, O. Polverino and R. Trombetti). Finite Fields Appl. (2015) preprint.
Geometry of the inversion in a finite field and partitions of PG(2^k-1,q) in normal rational curves (with C. Zanella). Journal of Geometry,(2014) preprint.
Orbits of the stabiliser group of the Segre variety product of three projective lines (with J. Sheekey). Finite Fields and Their Applications (2014), preprint.
Constant rank-distance sets of hermitian matrices and partial spreads in hermitian polar spaces (with R. Gow, J. Sheekey and F. Vanhove). Electronic Journal of Combinatorics (2014), preprint.
On embeddings of minimum dimension of \({\mathrm{PG}}(n,q)\times {\mathrm{PG}}(n,q)\) (with J. Sheekey and C. Zanella). Des. Codes Cryptogr. (2013) Available online.
Aspects of tensor products over finite fields and Galois geometries (with J. Sheekey). Proceedings of the Academy Contact Forum
{\em Galois Geometries and Applications} at the {\em Royal Flemish
Academy of Belgium for Science and the Arts} (October 5, 2012),
(2014), S. Nikova, B. Preneel and L. Storme, Eds., pp. 95--102 preprint
Solution to an isotopism question conerning rank 2 semifields (with G. Marino, O. Polverino and R. Trombetti). Journal of Combinatorial Designs (2015). preprint on arXiv.
Segre embeddings and finite semifields (with C. Zanella). Finite Fields Appl. (2014)
preprint.
Scattered linear sets and pseudoreguli (with G. Van de Voorde). Electronic Journal of Combinatorics. (2013) preprint
On the rank of 3x3x3-tensors (with A. Pavan and C. Zanella). Linear Multilinear Algebra (2012). preprint
Finite semifields and nonsingular tensors. Des. Codes Cryptogr. (2013) preprint
Semifields from skew polynomial rings (with J. Sheekey). Adv. Geom. (2013) preprint
F_q-pseudoreguli of PG(3,q^3) and scattered semifields of order q^6 (with G. Marino, O. Polverino and R. Trombetti). Finite Fields Appl. (2011).
preprint
Linear codes from projective spaces (with G. Van de Voorde en L. Storme).
Proceedings of the Conference on Error-Correcting Codes, Cryptography
and Finite Geometries, AMS book seriess (2010). preprint
Finite semifields with a large nucleus and higher secant varieties to Segre varieties. Adv. Geom. (2011). preprint
On linear sets on a projective line (with G. Van de Voorde). Des. Codes Cryptogr. (2010). preprint
A proof of the linearity conjecture for k-blockings sets in PG(n,q^3), q prime (with L. Storme and G. Van de Voorde). J. Combin. Theory Ser. A (2011). preprint
An empty interval in the spectrum of small weight codewords in the code from points and k-spaces of PG(n,q). J. Combin. Theory Ser. A (available online 29 January 2009) (with L. Storme, P. Sziklai and G. Van de Voorde). preprint
On the isotopism classes of finite semifields. Finite Fields Appl. 14 (2008) 897--910. preprint
On the code generated by the incidence matrix of points and k-spaces in PG(n, q) and its dual. Finite Fields and Appl. 14 (2008) 1020--1038 (with L. Storme and G. Van de Voorde). preprint
On the Hughes-Kleinfeld and Knuth's semifields two dimensional over a weak nucleus. Des. Codes Cryp
togr. 44 (2007), no. 1-3, 63--67 (with S. Ball). preprint
A geometric construction of finite semifields. J. Algebra 311 (2007), no. 1, 117--129 (with G.
Ebert and S. Ball). preprint
How to use Redei polynomials in higher dimensional spaces, with S. Ball, Le Matematiche (Catani
a), 59 (2004), 39--52 (2006). preprint
On the graph of a function in two variables over a finite field, with S. Ball, J. Algebraic Combin. 23 (2006) 243--253. preprint
Sublines of prime order contained in the set of internal points of a conic. Des. Codes Cryptogr. 38 (2006), no. 1, 113--123. preprint
The two sets of three semifields associated with a semifield flock. Innov. Incidence Geom. 2 (2
005), 101--107. preprint
Characterizations and properties of good eggs in PG(4n-1,q), q odd, Discrete Math. 301, (2005), 106--116. preprint
BLT-sets admitting the symmetric group S_4, with M. Law, Australasian J. Combinatorics, 33 (200
5), 307--316. preprint
Semifield flocks, eggs, and ovoids of Q(4,q), Adv. Geom. 5 (2005), no. 3, 333--345. preprint
Good Eggs and Veronese Varieties, with G. Lunardon, Discrete Math. 294 (2005), no. 1-2, 119--12
2. preprint
Eggs in PG(4n-1,q), q even, containing a pseudo pointed conic, with M. R. Brown, European J. Combin
. 26 (2005), no.1, 117--128. preprint
Good Eggs and Veronese Varieties, with G. Lunardon, Discrete Math. 294 (2005), no. 1-2, 119--12
Eggs in PG(4n-1,q), q even, containing a pseudo-conic, with M. R. Brown, Bull. London Math. Soc. 36 (2004), no. 5, 633--639. preprint
Symplectic Spreads, with S. Ball, J. Bamberg and T. Penttila, Des. Codes Cryptogr. 33 (2004) 9-
-14. preprint
On the classification of semifield flocks, with Simeon Ball and Aart Blokhuis, Adv. Math. 180 (
2003) 104--111. preprint
Commutative semifields of rank 2 over their middle nucleus, with Simeon Ball, Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, Mullen, G. L. (ed) et al, Springer-Verlag, 1--21, 2002. preprint
On eggs and translation generalised quadrangles, with Tim Penttila, J. Combin. Theory Ser. A 96
(2001), no. 2, 303--315. preprint
Linear (q+1)-fold blocking sets in PG(2,q4),
with Simeon Ball and Aart Blokhuis, Finite Fields Appl. 6 (2000), no. 4, 294--301. preprint
Scattered spaces with respect to a spread in PG(n,q), with Aart Blokhuis, Geom. Dedicata 81 (2000), no. 1-3, 231--243. preprint
special issues
Special issue on finite geometries. Edited by I. Cardinali, M. Lavrauw, K. Metsch, A. Pott. Des. Codes Cryptogr. 87 (2019).
Editorial on finite geometries. Ghinelli, D., Jungnickel, D., Lavrauw, M., Pott A. Des. Codes Cryptogr. (2016)
Special issue on finite geometries in honor of Frank de Clerck. Edited by J. Bamberg, J. De Beule, N. Durante, M. Lavrauw. Des. Codes Cryptogr. (2014)
conference proceedings
Theory and applications of finite fields. Proceedings of the 10th International Conference on Finite Fields and Their Applications (Fq 10) held in Ghent, July 11-15, 2011. Edited by Michel Lavrauw, Gary L. Mullen, Svetla Nikova, Daniel Panario and Leo Storme. Contemporary Mathematics, 579. American Mathematical Society, Providence, RI, 2012. viii+204 pp. ISBN: 978-0-8218-5298-9. Available from the AMS bookstore.
book
Scattered Spaces and Eggs in Finite Projective Spaces, Topics in Finite Geometry VDM Verlag Dr. Muller Aktiengesellschaft & Co. KG (2008) ISBN-10: 363906397X, ISBN-13: 978-3
639063974 (Available from amazon)
chapter in book
Finite Semifields (with Olga Polverino) preprint Chapter in Current Research Topics in Galois Geometries (NOVA collected works, Eds. Jan De Beule and L. Storme) (2011) website
PhD thesis
Scattered spaces with respect to spreads and eggs in finite projective spaces. (2001) pdf Technische Universiteit Eindhoven, The Netherlands. Advisors: Aart Blokhuis and Andries Brouwer.
