UC Research Profile - University of Canterbury

Dr Geertrui Van de Voorde

Contact

Department: Mathematics and Statistics

Email: geertrui.vandevoorde@canterbury.ac.nz

Direct Dial: +64 3 3695641

Office: Jack Erskine 724

Languages: English, Dutch

About

Research / Creative works

Supervision

Networks

Fields of Research

Finite projective geometry
Coding theory
Graph theory

Researcher Summary

My main research interest is finite projective geometry. In particular, I study the interplay between the combinatorial properties of particular sets and their algebraic description.

Moreover, I am interested in the links between finite geometry and other areas. Many open problems in coding theory can be translated into a purely geometrical problem. Similarly, examples of (extremal) graphs often arise from finite geometry.

Subject Area: Disciplines

Mathematics: Pure Mathematics

Prizes and Awards

Early Career Researcher Award ( 2020 - present )

New and Emerging Researcher Award 2020 ( 2021 - present )

PhD fellowship ( 2008 - 2010)

PhD fellowship ( 0 )

Post-doctoral fellowship ( 2012 - 2017)

Research/Scholarly/Creative Works

Journal Articles

De Boeck M. and Van de Voorde G. (2023) Embedded antipodal planes and the minimum weight of the dual code of points and lines in projective planes of order p². Designs, Codes, and Cryptography 91(3): 895-920. http://dx.doi.org/10.1007/s10623-022-01131-2.

Denaux L., D'haeseleer J. and Van de Voorde G. (2023) A higgledy-piggledy set of planes based on the ABB-representation of linear sets. Discrete Mathematics 346(12) 113603 http://dx.doi.org/10.1016/j.disc.2023.113603.

Faulkner J. and Van de Voorde G. (2023) On the equivalence, stabilisers, and feet of Buekenhout-Tits unitals. Designs, Codes, and Cryptography http://dx.doi.org/10.1007/s10623-023-01234-4.

De Boeck M. and Van de Voorde G. (2022) The weight distributions of linear sets in PG(1,q⁵). Finite Fields and their Applications 82 http://dx.doi.org/10.1016/j.ffa.2022.102034.

Jena D. and Van de Voorde G. (2022) The geometric field of linearity of linear sets. Designs, Codes, and Cryptography 90(3): 779-799. http://dx.doi.org/10.1007/s10623-022-01011-9.

Lavrauw M. and Van de Voorde G. (2022) LOCALLY REPAIRABLE CODES WITH HIGH AVAILABILITY BASED ON GENERALISED QUADRANGLES. Advances in Mathematics of Communications 16(1): 73-81. http://dx.doi.org/10.3934/amc.2020099.

Schillewaert J. and Van de Voorde G. (2022) Characterising elliptic and hyperbolic hyperplanes of the parabolic quadric Q(2n,q). Finite Fields and their Applications 78 http://dx.doi.org/10.1016/j.ffa.2021.101961.

Schillewaert J. and Van de Voorde G. (2022) Quasi-polar spaces. Combinatorial Theory 2(3) http://dx.doi.org/10.5070/c62359153.

Sheekey J., Van De Voorde G. and Voloch JF. (2022) ON THE PRODUCT OF ELEMENTS WITH PRESCRIBEDÂ TRACE. Journal of the Australian Mathematical Society 112(2): 264-288. http://dx.doi.org/10.1017/S1446788720000178.

De Boeck M. and Van De Voorde G. (2021) A note on large Kakeya sets. Advances in Geometry 21(3): 401-405. http://dx.doi.org/10.1515/advgeom-2021-0018.

Jena D. and Van de Voorde G. (2021) On linear sets of minimum size. Discrete Mathematics 344(3) http://dx.doi.org/10.1016/j.disc.2020.112230.

D’haeseleer J. and Van de Voorde G. (2020) Translation hyperovals and F2-linear sets of pseudoregulus type. Electronic Journal of Combinatorics 27(3): 1-19. http://dx.doi.org/10.37236/8818.

Metsch K. and Van de Voorde G. (2020) On a question of Thas on partial 3-(qⁿ + 1, q + 1, 1) designs. Journal of Combinatorial Designs 28(1): 25-32. http://dx.doi.org/10.1002/jcd.21678.

Sheekey J. and Van de Voorde G. (2020) Rank-metric codes, linear sets, and their duality. Designs, Codes, and Cryptography 88(4): 655-675. http://dx.doi.org/10.1007/s10623-019-00703-z.

De Beule J. and Van de Voorde G. (2019) The minimum size of a linear set. Journal of Combinatorial Theory. Series A 164: 109-124. http://dx.doi.org/10.1016/j.jcta.2018.12.008.

de Boeck M. and van de Voorde G. (2019) Elation KM-Arcs. Combinatorica 39(3): 501-544. http://dx.doi.org/10.1007/s00493-018-3806-1.

De Boeck M. and Van de Voorde G. (2018) A new lower bound for the size of an affine blocking set. The Electronic Journal of Combinatorics 25(4) P4.40: 11.

D’haeseleer J., Metsch K., Storme L. and Van de Voorde G. (2017) On the maximality of a set of mutually orthogonal Sudoku Latin Squares. Designs, Codes and Cryptography 84(1-2): 143-152. http://dx.doi.org/10.1007/s10623-016-0234-3.

Rottey S. and Van de Voorde G. (2017) Unitals with many Baer secants through a fixed point. Advances in Geometry : 10. http://dx.doi.org/10.1515/advgeom-2017-0010.

De Beule J., Héger T., Szőnyi T. and Van de Voorde G. (2016) Blocking and Double Blocking Sets in Finite Planes. The Electronic Journal of Combinatorics 23(2) P2.5.

De Boeck M. and Van de Voorde G. (2016) A linear set view on KM-arcs. Journal of Algebraic Combinatorics 44(1): 131-164. http://dx.doi.org/10.1007/s10801-015-0661-7.

Van de Voorde G. (2016) Constructing Minimal Blocking Sets Using Field Reduction. Journal of Combinatorial Designs 24(1): 36-52. http://dx.doi.org/10.1002/jcd.21432.

Van de Voorde G. (2016) Desarguesian spreads and field reduction for elements of the semilinear group. Linear Algebra and its Applications 507: 96-120. http://dx.doi.org/10.1016/j.laa.2016.05.038.

De Winter S., Rottey S. and Van de Voorde G. (2015) Linear representations of subgeometries. Designs, Codes and Cryptography 77(1): 203-215. http://dx.doi.org/10.1007/s10623-014-9999-4.

Rottey S. and Van de Voorde G. (2015) Characterisations of elementary pseudo-caps and good eggs. The Electronic Journal of Combinatorics 22(1) P1.49.

Rottey S. and Van de Voorde G. (2015) Pseudo-ovals in even characteristic and ovoidal Laguerre planes. Journal of Combinatorial Theory, Series A 129: 105-121. http://dx.doi.org/10.1016/j.jcta.2014.10.001.

Rottey S., Sheekey J. and de Voorde GV. (2015) Subgeometries in the Andre/Bruck-Bose representation. Finite Fields and Their Applications 35: 115-138. http://dx.doi.org/10.1016/j.ffa.2015.04.002.

Cara P., Rottey S. and Van de Voorde G. (2014) A construction for infinite families of semisymmetric graphs revealing their full automorphism group. Journal of Algebraic Combinatorics 39(4): 967-988. http://dx.doi.org/10.1007/s10801-013-0475-4.

Cara P., Rottey S. and Van de Voorde G. (2014) The isomorphism problem for linear representations and their graphs. Advances in Geometry 14(2): 353-367. http://dx.doi.org/10.1515/advgeom-2013-0040.

Lavrauw M. and Van de Voorde G. (2013) Scattered linear sets and pseudoreguli. The Electronic Journal of Combinatorics 20(1) P15.

Penttila T. and Van de Voorde G. (2013) Extending pseudo-arcs in odd characteristic. Finite Fields and Their Applications 22: 101-113. http://dx.doi.org/10.1016/j.ffa.2013.03.002.

Sziklai P. and Van de Voorde G. (2013) A small minimal blocking set in PG(n, p (t) ), spanning a (t-1)-space, is linear. Designs, Codes and Cryptography 68(1-3): 25-32. http://dx.doi.org/10.1007/s10623-012-9751-x.

Lavrauw M., Storme L. and de Voorde GV. (2011) A proof of the linearity conjecture for k-blocking sets in PG(n, p(3)), p prime. JOURNAL OF COMBINATORIAL THEORY SERIES A 118 3: 808-818. http://dx.doi.org/10.1016/j.jcta.2010.11.013.

Van de Voorde G. (2011) On sets without tangents and exterior sets of a conic. DISCRETE MATHEMATICS 311 20: 2253-2258. http://dx.doi.org/10.1016/j.disc.2011.07.010.

Dodunekov S., Storme L. and Van de Voorde G. (2010) Partial covers of PG(n, q). EUROPEAN JOURNAL OF COMBINATORICS 31 6, SI: 1611-1616. http://dx.doi.org/10.1016/j.ejc.2009.07.008.

Lavrauw M. and Van de Voorde G. (2010) On linear sets on a projective line. DESIGNS CODES AND CRYPTOGRAPHY 56 2-3: 89-104. http://dx.doi.org/10.1007/s10623-010-9393-9.

Pepe V., Storme L. and Van de Voorde G. (2010) On codewords in the dual code of classical generalised quadrangles and classical polar spaces. DISCRETE MATHEMATICS 310 22, SI: 3132-3148. http://dx.doi.org/10.1016/j.disc.2009.06.010.

Van de Voorde G. (2010) On the linearity of higher-dimensional blocking sets. ELECTRONIC JOURNAL OF COMBINATORICS 17 1.

Lavrauw M., Storme L., Sziklai P. and de Voorde GV. (2009) An empty interval in the spectrum of small weight codewords in the code from points and k-spaces of PG(n, q). JOURNAL OF COMBINATORIAL THEORY SERIES A 116 4: 996-1001. http://dx.doi.org/10.1016/j.jcta.2008.09.004.

Pepe V., Storme L. and Van de Voorde G. (2009) Small Weight Codewords in the LDPC Codes Arising From Linear Representations of Geometries. JOURNAL OF COMBINATORIAL DESIGNS 17 1: 1-24. http://dx.doi.org/10.1002/jcd.20179.

Fack V., Fancsali SL., Storme L., Van de Voorde G. and Winne J. (2008) Small weight codewords in the codes arising from Desarguesian projective planes. DESIGNS CODES AND CRYPTOGRAPHY 46 1: 25-43. http://dx.doi.org/10.1007/s10623-007-9126-x.

Lavrauw M., Storme L. and de Voorde GV. (2008) On the code generated by the incidence matrix of points and hyperplanes in PG(n,q) and its dual. DESIGNS CODES AND CRYPTOGRAPHY 48 3: 231-245. http://dx.doi.org/10.1007/s10623-008-9203-9.

Lavrauw M., Storme L. and Van de Voorde G. (2008) On the code generated by the incidence matrix of points and k-spaces in PG(n, q) and its dual. FINITE FIELDS AND THEIR APPLICATIONS 14 4: 1020-1038. http://dx.doi.org/10.1016/j.ffa.2008.06.002.

Conference Contributions - Published

Lavrauw M. and Van de Voorde G. (2015) Field reduction and linear sets in finite geometry. In Kyureghyan G; Mullen GL; Pott A (Eds). Topics in Finite Fields 632: 271-293. http://dx.doi.org/10.1090/conm/632/12633.

Lavrauw M., Storme L. and Van de Voorde G. (2010) Linear codes from projective spaces. In Bruen AA; Wehlau DL (Eds). ERROR-CORRECTING CODES, FINITE GEOMETRIES AND CRYPTOGRAPHY 523: 185-202.

Oral Presentations

Van de Voorde G. (2023) Point sets with few intersection numbers in projective spaces. San Diego, USA: Combinatorics Seminar Series, 02 May 2023.

Van de Voorde G. (2022) Quasi-Polar Spaces. Irsee, Germany: Finite Geometries (sixth Irsee conference), 02 Sep 2022.

Van de Voorde G. (2022) Quasi-quadrics in finite projective spaces. Perth, Australia: Combinatorics Seminar, 11 Nov 2022.

Van de Voorde G. (2022) The dual code of points and lines in a projective plane. Galway, Ireland: ILAS conference (International Linear Algebra Society), 21 Jun 2022.

Van de Voorde G. (2021) Codes from finite projective planes. Napier, NZ: NZMRI Summer meeting, 11 Jan 2021.

Van de Voorde G. (2021) Menelaos strikes again. University of Canterbury and online: NZMS mini-colloquium, 07 Dec 2021.

Van de Voorde G. (2021) The product of elements with prescribed trace. Online (organised by City University of New York): Combinatorial and Additive Number Theory, 27 May 2021.

Van de Voorde G. (2019) A geometric view on rank-metric codes. Auckland, New Zealand: Groups and Geometry, 18 Jan 2019.

Van de Voorde G. (2019) F2-linear sets, translation hyperovals and KM-arcs. Adelaide, Australia: Finite Geometry: a workshop in honour of Tim Penttila, 16 Dec 2019.

Van de Voorde G. (2019) Linear sets. Brussels, Belgium: Finite Geometry and Friends, 17 Jun 2019.

Van de Voorde G. (2019) On the (non)-existence of certain disjoint linear sets. Sydney, Australia: 42ACCMCC Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, 09 Dec 2022.

Van de Voorde G. (2019) On the product of elements with prescribed trace. Christchurch, NZ: NZ number theory workshop, 26 Aug 2019.

Van de Voorde G. (2018) Blocking sets in finite projective planes. Dunedin, New Zealand: Colloquium of the New Zealand Mathematical society, 04 Dec 2018.

Van de Voorde G. (2018) The number of directions determined by a function over a finite field. Rotorua, New Zealand: 41ACCMCC Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, 10 Dec 2018.

Van de Voorde GV. (2018) The tragedy of two Baer subplanes. Arco, Italy: Combinatorics 2018, 04 Jun 2018.

Van de Voorde GV. (2017) The number of directions determined by a function over a finite field. CoGeNt seminar, 02 May 2017.

Van de Voorde GV. (2017) The number of points of weight 2 in a linear set on a projective line. Irsee, Germany: Finite Geometries - Fifth Irsee conference (conference on invitation), 11 Sep 2017.

Van de Voorde G. (2016) Field reduction in finite projective geometry. Brussels (Belgium): Arithmetique en Plat Pays (getaltheorie in het vlakke land), 18 Apr 2016.

Van de Voorde GV. (2016) KM-arcs. Brussels, Belgium: Joint Seminar UGent-VUB-ULB, 17 Nov 2016.

Van de Voorde G. (2013) Field reduction in finite projective geometry. Magdeburg, Germany: FQ11 - International Conference on Finite Fields and their Applications, 22 Jul 2013.

Van de Voorde G. (2011) LDPC codes from finite geometries. Ghent, Belgium: Colloquium on Galois Geometry, 27 May 2011.

Student Supervision

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Current

PhD - Findlay R: 4-dimensional elation Laguerre planes of group dimension 9

Completed

PhD - D'Haeseleer J: Families of intersecting subspaces (2021)
PhD - Drummond G: Structured Circuits in Matroids (2022)
PhD - Jena D: Point sets in projective spaces: intersection numbers and linearity (2023)
PhD - Rottey S: Characterising substructures of finite projective spaces (2016)
Masters - Botteldoorn A: Codes from finite planes (2016)
Masters - D'haeseleer J: Subspace codes and their geometric background (2017)
Masters - Faulkner J: Unitals in projective planes (2023)
Summer Student - Chan M: Projective Planes and complete arcs (2022)
Summer Student - Faulkner J: Latin Hypercubes and Finite Projective Geometry (2021)
Summer Student - Walle D: Eigenvalue techniques for graph theory (2022)

Editorial Work

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Algebraic Combinatorics Editor ( 2017 - 2023)
Bulletin of the Belgian Mathematical Society: Simon Stevin Editor ( 2019 - 2023)
Bulletin of the Institute of Combinatorics and its Applications Editor ( 2017 - 2023)

Review and Refereeing

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Advances in Geometry ( 2021 - 2023)

Advances in Mathematics of Communications ( 2020 - 2023)

Algebraic Combinatorics ( 2018 - 2023)

Ars Mathematica Contemporanea ( 2018 - 2023)

Australasian Journal of Combinatorics ( 2013 - 2023)

Bulletin of the Institute of Combinatorics and its Applications ( 2017 - 2023)

Bulletin of the London Mathematical Society ( 2018 - 2023)

Combinatorica ( 2015 - 2023)

Designs, Codes, and Cryptography ( 2008 - 2023)

Discrete Mathematics ( 2010 - 2023)

European Journal of Combinatorics ( 2017 - 2023)

Finite Fields and Their Applications ( 2010 - 2023)

Innovations in Incidence Geometry ( 2017 - 2023)

Journal of Algebraic Combinatorics ( 2012 - 2023)

Journal of Combinatorial Designs ( 2010 - 2023)

Journal of Combinatorial Theory: Series A ( 2017 - 2023)

Mathematical Reviews database (MathSciNet) ( 2016 - 2023)

Zentralblatt fur Mathematik (zbMATH) ( 2015 - 2023)