Publications

On the size of a double blocking set in PG(2,q), Finite Fields Appl., 2 (1996) 125--137.
(with A. Blokhuis) pdf or ps or dvi file

On the size of a triple blocking set in PG(2,q), European J. Combin., 5 (1996) 427--435. pdf or ps or dvi file

Multiple blocking sets and arcs in finite planes, J. London Math. Soc., 54 (1996) 581--593. pdf or ps or dvi file

Maximal arcs in Desarguesian planes of odd order do not exist, Combinatorica, 17 (1997) 31--41.
(with A. Blokhuis and F. Mazzocca) pdf or ps or dvi file

On small complete arcs in a finite plane, Discrete Math., 174 (1997) 29--34. pdf or ps or dvi file

Partial unitals and related structures in Desarguesian planes, Des. Codes Cryptogr., 15 (1998) 231--236. pdf or ps or dvi file

An easier proof of the maximal arcs conjecture, Proc. Amer. Math. Soc., 126 (1998) 3377--3380.
(with A. Blokhuis) pdf or ps or dvi file

On nuclei and blocking sets in Desarguesian spaces, J. Combin. Theory Ser. A, 85 (1999) 232--237. pdf or ps or dvi file

On the incompleteness of (k,n)-arcs in Desarguesian planes of order q where n divides q, Geom. Dedicata, 74 (1999) 325--332.
(with A. Blokhuis) pdf or ps or dvi file

On the number of slopes of the graph of a function defined over a finite field, J. Combin. Theory Ser. A, 86 (1999) 187--196.
(with A. Blokhuis, A. E. Brouwer, L. Storme and T. Szonyi) pdf or ps or dvi file

Unitals with many Baer sublines, Des. Codes Cryptogr., 17 (1999) 237--252.
(with A. Blokhuis and C. M. O'Keefe) pdf or ps or dvi file

Polynomials in finite geometries, in: Surveys in combinatorics, 1999, Lamb, J. D. (ed) et al, Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 267, 17--35, 1999. pdf or ps or dvi file

Polynomials in finite geometry, in: Methods of Discrete Mathematics, 1999, Lowe, S. (ed) et al, Quaderni di mathematica, Napoli, volume 5, 71--101, 1999.
(with A. Blokhuis)

On intersection sets in Desarguesian affine spaces, European J. Combin., 21 (2000) 441--446. pdf or ps or dvi file

Linear (q+1)-fold blocking sets in PG(2,q^4), Finite Fields Appl., 6 (2000) 294--301.
(with A. Blokhuis and M. Lavrauw)

On (q²+q+2,q+2)-arcs in the projective plane PG(2,q), Des. Codes Cryptogr., 24 (2001) 205--224.
(with R. Hill, I. Landjev and H. Ward)

The classification of maximal arcs in small Desarguesian planes, Bull. Belg. Math. Soc., 9 (2002) 433--445.
(with A. Blokhuis) pdf or ps or dvi file

Commutative semifields of rank 2 over their middle nucleus, in: Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, Mullen, G. L. (ed) et al, Springer-Verlag, 1--21, 2002.
(with M. Lavrauw) pdf

On the classification of semifield flocks, Adv. Math., 180 (2003) 104--111.
(with A. Blokhuis and M. Lavrauw) pdf or ps or dvi file

The number of directions determined by a function over a finite field, J. Combin. Theory Ser. A, 104 (2003) 341--350. pdf or ps or dvi file

On ovoids of O(5,q), Adv. Geom., 4 (2004) 1--7. pdf or ps or dvi file

Symplectic spreads and permutation polynomials, in: Finite Fields and Applications, Mullen, G. L. (ed) et al, Springer-Verlag, 79--88, 2004.
(with M. Zieve) pdf or ps or dvi file

Symplectic spreads, Des. Codes Cryptogr., 32 (2004) 9--14.
(with J. Bamberg, M. Lavrauw and T. Penttila) pdf or ps or dvi file

The six semifield planes associated with a semifield flock, Adv. Math., 189 (2004) 68--87.
(with M. Brown) pdf or ps or dvi file

Bounds on (n,r)-arcs and their application to linear codes, Finite Fields Appl., 11 (2005) 326--336.
(with J. W. P. Hirschfeld) pdf or ps or dvi file

On ovoids of parabolic quadrics, Des. Codes Cryptogr., 38 (2006) 131--145.
(with P. Govaerts and L. Storme) pdf or ps or dvi file

How to use Redei polynomials in higher dimensional spaces, Le Matematiche (Catania), 59 (2004) 39--52 (2006).
(with M. Lavrauw) pdf or ps or dvi file

On ovoids of PG(3,q), Adv. Geom., 6 (2006) 177--198. pdf or ps or dvi file


On the graph of a function in two variables over a finite field, J. Algebraic Combin., 23 (2006) 243--253.
(with M. Lavrauw) pdf or ps or dvi file

Introducció als polinomis de Rédei, Butl. Soc. Catalana Mat., 21 (2006) 197--211. pdf

Affine blocking sets, three dimensional codes and the Griesmer bound, Discrete Math., 307 (2007) 1600--1608.
(with E. Montanucci) pdf or ps or dvi file

Functions over finite fields that determine few directions, Electr. Notes in Discrete Math., 29 (2007) 185--188. pdf or ps or dvi file

On linear codes whose weights and length have a common divisor, Adv. Math., 211 (2007) 94--104.
(with A. Blokhuis, A. Gacs, P. Sziklai and Zs. Weiner) pdf or ps or dvi file

A geometric construction of finite semifields, J. Algebra, 311 (2007) 117--129.
(with G. Ebert and M. Lavrauw) pdf or ps or dvi file

On the Hughes-Kleinfeld and Knuth's semifields two dimensional over a weak nucleus, Des. Codes Cryptogr., 44 (2007) 63--67.
(with M. Lavrauw) pdf or ps or dvi file

On the graph of a function in many variables over a finite field, Des. Codes Cryptogr., 47 (2008) 159--164. pdf or ps or dvi file

On the number of directions determined by a pair of functions over a prime field, J. Combin. Theory Ser. A, 115 (2008) 505--516.
(with A. Gacs and P. Sziklai) pdf or ps or dvi file

On sets of points in a finite affine plane containing a line in every direction, (2008), unpublished. pdf

On the graph of a function over a prime field whose small powers have bounded degree, European J. Combin., 30 (2009) 1575--1584.
(with A. Gacs) pdf or ps or dvi file

Multiple blocking sets in finite projective spaces and improvements to the Griesmer bound for linear codes, Des. Codes Cryptogr., 53 (2009) 119--136.
(with S. Fancsali) pdf or ps or dvi file

Punctured Combinatorial Nullstellensatze, Combinatorica, 29 (2009) 511--522.
(with O. Serra) pdf

The polynomial method in Galois geometries, in Current research topics in Galois geometry, Chapter 5, Nova Sci. Publ., New York, (2012) 105--130. pdf or ps or dvi file

On sets of vectors of a finite vector space in which every subset of basis size is a basis, J. Eur. Math. Soc., 14 (2012) 733--748. pdf

Asymptotic improvements to the lower bound of certain bipartite Turan numbers, Combin. Probab. Comput., 21 (2012) 323--329. pdf
(with V. Pepe)

On sets of vectors of a finite vector space in which every subset of basis size is a basis II, Des. Codes Cryptogr., 65 (2012) 5--14. pdf
(with J. De Beule)

An alternative way to generalise the pentagon, J. Combin. Des., 21 (2013) 163--179. pdf
(with J. Bamberg, A. Devillers and K. Stokes)

A bound for the maximum weight of a linear code, SIAM J. Discrete Math., 27 (2013) 575--583. pdf
(with A. Blokhuis)

Lacunary polynomials over finite fields, in Handbook of Finite Fields, 2013. pdf
(with A. Blokhuis)

On the representability of the bi-uniform matroid, SIAM J. Discrete Math., 27 (2013) 1482--1491. pdf
(with C. Padro, Zs. Weiner and C. Xing)

A p-adic condition on the weight of a codeword of a linear code, Des. Codes Cryptogr., 72 (2014) 177--183. pdf


Rédei polynomials over fields of characteristic zero, in Galois Geometries and Applications, Koninklijke Vlaamse Academie Van Beligie voor Wetenschappen en Kunsten (2014) 11--17. pdf


Finite Geometry and Combinatorial Applications, London Mathematical Society Student Texts 82, Cambridge University Press, 2015. ISBN 978-1-316-25744-9. US or not US


Forbidden subgraphs in the norm graph, Discrete Math., 339 (2016) 1206--1211. pdf
(with V. Pepe)

A finite version of the Kakeya problem, Australasian Journal of Combinatorics, 65 (2016) 251--260. pdf
(with A. Blokhuis and D. Domenzain)

On subsets of the normal rational curve, IEEE Transactions on Information Theory , 63 (2017) 3658--3662. pdf
(with J. De Beule)

On arcs and quadrics, in: Arithmetic of Finite Fields. WAIFI 2016. Lecture Notes in Computer Science, Springer, Cham., 10064 (2017) 95--102. pdf


A generalisation of Sylvester's problem to higher dimensions, J. Geom., 108 (2017) 529--543. pdf
(with J. Monserrat)

Extending small arcs to large arcs, European Journal of Mathematics, 4 (2018) 8--25. pdf


On sets defining few ordinary planes, Discrete Comput. Geom., 60 (2018) 220--253. pdf


Review of Larry Guth's "Polynomial Methods in Combinatorics" in Jahresbericht der Deutschen Mathematiker-Vereinigung, 120 (2018) 147--150. pdf


Planar arcs, J. Combin. Theory Ser. A, 160 (2018) 261--287. pdf
(with M. Lavrauw)

Arcs in finite projective spaces, EMS Surveys in Mathematical Science, 6 (2019) 133--172. pdf
(with M. Lavrauw)

Arcs and tensors, Des. Codes Cryptogr., 88 (2020) 17--31. pdf
(with M. Lavrauw)

On sets of points with few odd secants, Combinatorics, Probability, Computing, 29 (2020) 31--43. pdf
(with B. Csajbok)

A Course in Algebraic Error-Correcting Codes, Compact Textbooks in Mathematics, Birkhauser, 2020. ISBN 978-3-030-41152-7

On varieties defined by large sets of quadrics and their application to error-correcting codes, Discrete Math., 343 (2020) Article 112007. pdf
(with V. Pepe)

Some constructions of quantum MDS codes, Des. Codes Cryptogr., 89 (2021) 811--821.pdf


On sets defining few ordinary solids, Discrete Comput. Geom., 66 (2021) 68--91. pdf
(with E. Jimenez)


A polynomial time reduction from the multi-graph isomorphism problem to additive code equivalence, Discrete Math. Lett., 8 (2022) 66--68. pdf
(with J. Dixon)


The geometry of Hermitian self-orthogonal codes, J. Geom, 113, Article number: 7 (2022). pdf
(with R. Vilar)


Determining when a truncated generalised Reed-Solomon code is Hermitian self-orthogonal, IEEE Transactions on Information Theory, 68 (2022) 3796--3805. pdf
(with R. Vilar)


The equivalence of linear codes implies semi-linear equivalence, Des. Codes Cryptogr., 90 (2022), 1557--1565. pdf
(with J. Dixon)


On additive MDS codes over small fields, Adv. Math. Commun., 17 (2023) 828--844. pdf
(with G. Gamboa and M. Lavrauw)


Quantum error-correcting codes and their geometries, . Ann. Inst. Henri Poincare Comb. Phys. Interact., Ann. Inst. Henri Poincare D 10 (2023), no. 2, 337--405. pdf
(with A. Centelles and F. Huber)


The Grassl-Rotteler cyclic and consta-cyclic MDS codes are generalised Reed-Solomon codes, Des. Codes Cryptogr., 91 (2023) 1685--1694. pdf


On additive MDS codes with linear projections, Finite Fields Appl., 91 (2023) 102255. pdf
(with S. Adriaensen)


A Course in Combinatorics and Graphs, Compact Textbooks in Mathematics, Birkhauser, 2024, ISBN: 978-3-031-55383-7.
(with O. Serra)


Stabiliser codes over fields of even order, IEEE Transactions on Information Theory, 71 (2025) 3707--3718. pdf
(with E. Moreno and R. Simoens)


Griesmer type bounds for additive codes over finite fields, integral and fractional MDS codes, Des. Codes Cryptogr., 93 (2025) 175--196. pdf
(with M. Lavrauw and T. Popatia)


Ovoids in the cyclic presentation of PG(3,q), Des. Codes Cryptogr., 93 (2025) 4765--4778. pdf
(with K.Abdukhalikov, D. Ho and T. Popatia)


Additive codes from linear codes, IEEE Transactions on Information Theory, 72 (2026) 342--345. pdf
(with T. Popatia)


Classical and quantum cyclic redundancy check codes, Adv. Math. Comm., 21 (2026) 75--94. pdf
(with R. Vilar)


Error-correcting codes and absolutely maximally entangled states for mixed dimensional Hilbert spaces, Phys. Rev. A, 113 (2026) 012432. pdf.
(with R. Zhang)


Practical implementation of geometric quasi-cyclic LDPC codes, preprint. pdf
(with T. Ortega)


Geometrical constructions of purity testing protocols and their applications to quantum communication, preprint. pdf.
(with D. Glynn, R. Trenyi and M. Curty)


Thirty-six quantum officers are entangled, preprint. pdf
(with R. Simoens)

Updated 4 March 2026