Leo Storme

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The characterisation of the smallest two fold blocking sets in PG(n, 2)
- Manohar L. Aggarwal
  Department of Mathematical Sciences, The University of Memphis, Memphis, USA 38152
  ,
- Andreas Klein
  Department of Mathematics, Ghent University, Ghent, Belgium 9000
  ,
- Leo Storme
  Department of Mathematics, Ghent University, Ghent, Belgium 9000
Designs, Codes and Cryptography, Volume 63, Issue 2•May 2012, pp 149-157 • https://doi.org/10.1007/s10623-011-9541-x

We classify the smallest two fold blocking sets with respect to the ( n k )-spaces in PG( n , 2). We show that they either consist of two disjoint k -dimensional subspaces or are equal to a ( k + 1)-dimensional space minus one point.
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Theorems of Erdős-Ko-Rado type in polar spaces
- Valentina Pepe
  Department of Mathematics, Ghent University, Krijgslaan 281-S22, 9000 Ghent, Belgium
  ,
- Leo Storme
  Department of Mathematics, Ghent University, Krijgslaan 281-S22, 9000 Ghent, Belgium
  ,
- Frédéric Vanhove
  Department of Mathematics, Ghent University, Krijgslaan 281-S22, 9000 Ghent, Belgium
Journal of Combinatorial Theory Series A, Volume 118, Issue 4•May, 2011, pp 1291-1312 • https://doi.org/10.1016/j.jcta.2011.01.003

We consider Erdos-Ko-Rado sets of generators in classical finite polar spaces. These are sets of generators that all intersect non-trivially. We characterize the Erdos-Ko-Rado sets of generators of maximum size in all polar spaces, except for H(4n+1,q^2)...
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Galois geometries and applications
- Jan Beule
  Ghent University, Ghent, Belgium
  ,
- Yves Edel
  Ghent University, Ghent, Belgium
  ,
- Emilia Käsper
  K.U. Leuven, Leuven, Belgium
  ,
- Andreas Klein
  Ghent University, Ghent, Belgium
  ,
- Svetla Nikova
  K.U. Leuven, Leuven, Belgium
  ,
- Bart Preneel
  K.U. Leuven, Leuven, Belgium
  ,
- Jeroen Schillewaert
  Ghent University, Ghent, Belgium
  ,
- Leo Storme
  Ghent University, Ghent, Belgium
Designs, Codes and Cryptography, Volume 56, Issue 2-3•August 2010, pp 85-86 • https://doi.org/10.1007/s10623-010-9410-z
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In memoriam, András Gács
- Simeon Ball
  Universitat Politècnica de Catalunya, Barcelona, Spain
  ,
- Jan De Beule
  Ghent University, Ghent, Belgium
  ,
- Leo Storme
  Ghent University, Ghent, Belgium
  ,
- Peter Sziklai
  Eötvös Loránd University, Budapest, Hungary
  ,
- Tamás Szőnyi
  Eötvös Loránd University, Budapest, Hungary
Designs, Codes and Cryptography, Volume 56, Issue 2-3•August 2010, pp 87-88 • https://doi.org/10.1007/s10623-010-9409-5
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A study of (x(q + 1), x; 2, q)-minihypers
- Ivan Landjev
  Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria 1113 and New Bulgarian University, Sofia, Bulgaria 1618
  ,
- Leo Storme
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
Designs, Codes and Cryptography, Volume 54, Issue 2•February 2010, pp 135-147 • https://doi.org/10.1007/s10623-009-9314-y

In this paper, we study the weighted ( x ( q + 1), x ; 2, q )-minihypers. These are weighted sets of x ( q + 1) points in PG(2, q ) intersecting every line in at least x points. We investigate the decomposability of these minihypers, and ...
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A spectrum result on maximal partial ovoids of the generalized quadrangle Q(4,q), q even
- C. Röíing
  School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
  ,
- L. Storme
  Ghent University, Department of Pure Mathematics and Computer Algebra, Krijgslaan 281-S22, 9000 Ghent, Belgium
European Journal of Combinatorics, Volume 31, Issue 1•January, 2010, pp 349-361 • https://doi.org/10.1016/j.ejc.2009.01.003

This article presents a spectrum result on maximal partial ovoids of the generalized quadrangle Q(4,q), q even. We prove that for every integer k in an interval of, roughly, size [q^2/10,9q^2/10], there exists a maximal partial ovoid of size k on Q(4,q),...
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An empty interval in the spectrum of small weight codewords in the code from points and k-spaces of PG(n,q)
- Michel Lavrauw
  Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, 9000 Ghent, Belgium
  ,
- Leo Storme
  Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, 9000 Ghent, Belgium
  ,
- Peter Sziklai
  Department of Computer Science, Eötvös Loránd University, Pázmány P. sétány 1/C, H-1117 Budapest, Hungary
  ,
- Geertrui Van de Voorde
  Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, 9000 Ghent, Belgium
Journal of Combinatorial Theory Series A, Volume 116, Issue 4•May, 2009, pp 996-1001 • https://doi.org/10.1016/j.jcta.2008.09.004

Let C"k(n,q) be the p-ary linear code defined by the incidence matrix of points and k-spaces in PG(n,q), q=p^h, p prime, h>=1. In this paper, we show that there are no codewords of weight in the open interval ]q^k^+^1-1q-1,2q^k[ in C"k(n,q)@?C"n"-"k(n,q)...
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Generalised dual arcs and Veronesean surfaces, with applications to cryptography
- A. Klein
  Ghent University, Department of Pure Mathematics and Computer Algebra, Krijgslaan 281-S22, 9000 Ghent, Belgium
  ,
- J. Schillewaert
  Ghent University, Department of Pure Mathematics and Computer Algebra, Krijgslaan 281-S22, 9000 Ghent, Belgium
  ,
- L. Storme
  Ghent University, Department of Pure Mathematics and Computer Algebra, Krijgslaan 281-S22, 9000 Ghent, Belgium
Journal of Combinatorial Theory Series A, Volume 116, Issue 3•April, 2009, pp 684-698 • https://doi.org/10.1016/j.jcta.2008.11.001

We start by defining generalised dual arcs, the motivation for defining them comes from cryptography, since they can serve as a tool to construct authentication codes and secret sharing schemes. We extend the characterisation of the tangent planes of ...
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Tight sets, weighted m-covers, weighted m-ovoids, and minihypers
- Jan Beule
  Department of Pure Mathematics and Computer Algebra, Ghent University, Gent, Belgium 9000
  ,
- Patrick Govaerts
  Department of Pure Mathematics and Computer Algebra, Ghent University, Gent, Belgium 9000
  ,
- Anja Hallez
  Department of Pure Mathematics and Computer Algebra, Ghent University, Gent, Belgium 9000
  ,
- Leo Storme
  Department of Pure Mathematics and Computer Algebra, Ghent University, Gent, Belgium 9000
Designs, Codes and Cryptography, Volume 50, Issue 2•February 2009, pp 187-201 • https://doi.org/10.1007/s10623-008-9223-5

Minihypers are substructures of projective spaces introduced to study linear codes meeting the Griesmer bound. Recently, many results in finite geometry were obtained by applying characterization results on minihypers (De Beule et al. 16:342---349, 2008;...
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Characterization results on arbitrary non-weighted minihypers and on linear codes meeting the Griesmer bound
- J. Beule
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
  ,
- K. Metsch
  Mathematisches Institut, Justus-Liebig-Universität, Giessen, Germany 35392
  ,
- L. Storme
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
Designs, Codes and Cryptography, Volume 49, Issue 1-3•December 2008, pp 187-197 • https://doi.org/10.1007/s10623-008-9191-9

We present characterization results on non-weighted minihypers. For minihypers in PG( k 1, q ), q not a square, we improve greatly the results of Hamada, Helleseth, and Maekawa, and of Ferret and Storme. The largest improvements are obtained for q ...
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On the code generated by the incidence matrix of points and hyperplanes in PG(n,q) and its dual
- Michel Lavrauw
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
  ,
- Leo Storme
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
  ,
- Geertrui Voorde
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
Designs, Codes and Cryptography, Volume 48, Issue 3•September 2008, pp 231-245 • https://doi.org/10.1007/s10623-008-9203-9

In this paper, we study the p -ary linear code C ( PG ( n , q )), q = p ^h, p prime, h 1, generated by the incidence matrix of points and hyperplanes of a Desarguesian projective space PG ( n , q ), and its dual code. We link the ...
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Partial ovoids and partial spreads in symplectic and orthogonal polar spaces
- J. De Beule
  Ghent University, Department of Pure Mathematics and Computer Algebra, Krijgslaan 281-S22, 9000 Ghent, Belgium
  ,
- A. Klein
  Ghent University, Department of Pure Mathematics and Computer Algebra, Krijgslaan 281-S22, 9000 Ghent, Belgium
  ,
- K. Metsch
  Justus-Liebig-Universität, Mathematisches Institut, Arndtstrasse 2, D-35392 Giessen, Germany
  ,
- L. Storme
  Ghent University, Department of Pure Mathematics and Computer Algebra, Krijgslaan 281-S22, 9000 Ghent, Belgium
European Journal of Combinatorics, Volume 29, Issue 5•July, 2008, pp 1280-1297 • https://doi.org/10.1016/j.ejc.2007.06.004

We present improved lower bounds on the sizes of small maximal partial ovoids and small maximal partial spreads in the classical symplectic and orthogonal polar spaces, and improved upper bounds on the sizes of large maximal partial ovoids and large ...
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Partial ovoids and partial spreads in hermitian polar spaces
- J. Beule
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
  ,
- A. Klein
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
  ,
- K. Metsch
  Mathematisches Institut, Justus-Liebig-Universität, Giessen, Germany 35392
  ,
- L. Storme
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
Designs, Codes and Cryptography, Volume 47, Issue 1-3•June 2008, pp 21-34 • https://doi.org/10.1007/s10623-007-9047-8

We present improved lower bounds on the sizes of small maximal partial ovoids in the classical hermitian polar spaces, and improved upper bounds on the sizes of large maximal partial spreads in the classical hermitian polar spaces. Of particular ...
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Small weight codewords in the codes arising from Desarguesian projective planes
- Veerle Fack
  Research Group on Combinatorial Algorithms and Algorithmic Graph Theory, Department of Applied Mathematics and Computer Science, Ghent University, Ghent, Belgium 9000
  ,
- Szabolcs L. Fancsali
  Department of Computer Science, Eötvös Loránd University, Budapest, Hungary 1117
  ,
- L. Storme
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
  ,
- Geetrui Voorde
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
  ,
- Joost Winne
  Research Group on Combinatorial Algorithms and Algorithmic Graph Theory, Department of Applied Mathematics and Computer Science, Ghent University, Ghent, Belgium 9000
Designs, Codes and Cryptography, Volume 46, Issue 1•January 2008, pp 25-43 • https://doi.org/10.1007/s10623-007-9126-x

We study codewords of small weight in the codes arising from Desarguesian projective planes. We first of all improve the results of K. Chouinard on codewords of small weight in the codes arising from PG (2, p ), p prime. Chouinard characterized all ...
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On the smallest maximal partial ovoids and spreads of the generalized quadrangles W(q) and Q(4,q)
- M. Cimráková
  Research Group on Combinatorial Algorithms and Algorithmic Graph Theory, Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000 Ghent, Belgium
  ,
- S. De Winter
  Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, B-9000 Ghent, Belgium
  ,
- V. Fack
  Research Group on Combinatorial Algorithms and Algorithmic Graph Theory, Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000 Ghent, Belgium
  ,
- L. Storme
  Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, B-9000 Ghent, Belgium
European Journal of Combinatorics, Volume 28, Issue 7•October, 2007, pp 1934-1942 • https://doi.org/10.1016/j.ejc.2006.11.001

We present results on the size of the smallest maximal partial ovoids and on the size of the smallest maximal partial spreads of the generalized quadrangles W(q) and Q(4,q).
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A weighted version of a result of Hamada on minihypers and on linear codes meeting the Griesmer bound
- I. Landjev
  New Bulgarian University, Sofia, Bulgaria 1618 and Institute of Mathematics and Informatics, BAS, Sofia, Bulgaria 1113
  ,
- L. Storme
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
Designs, Codes and Cryptography, Volume 45, Issue 1•October 2007, pp 123-138 • https://doi.org/10.1007/s10623-007-9093-2

Minihypers were introduced by Hamada to investigate linear codes meeting the Griesmer bound. Hamada (Bull Osaka Women's Univ 24:1---47, 1985; Discrete Math 116:229---268, 1993) characterized the non-weighted minihypers having parameters , with k -1 > ...
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Characterization results on small blocking sets of the polar spaces Q+(2n + 1, 2) and Q+(2n + 1, 3)
- J. Beule
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
  ,
- K. Metsch
  Mathematisches Institut, Justus-Liebig-Universität Gieβen, Gieβen, Germany D-35392
  ,
- L. Storme
  Department of Pure Mathematics and Computer Algebra, Ghent University, Ghent, Belgium 9000
Designs, Codes and Cryptography, Volume 44, Issue 1-3•September 2007, pp 197-207 • https://doi.org/10.1007/s10623-007-9087-0

In De Beule and Storme, Des Codes Cryptogr 39(3):323---333, De Beule and Storme characterized the smallest blocking sets of the hyperbolic quadrics Q ⁺(2 n + 1, 3), n 4; they proved that these blocking sets are truncated cones over the unique ...
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Blocking Sets in PG(r, qn)
- F. Mazzocca
  Dipartimento di Matematica, Seconda Università degli Studi di Napoli, Caserta, Italy I-81100
  ,
- O. Polverino
  Dipartimento di Matematica, Seconda Università degli Studi di Napoli, Caserta, Italy I-81100
  ,
- L. Storme
  Department of Pure Maths and Computer Algebra, Ghent University, Gent, Belgium 9000
Designs, Codes and Cryptography, Volume 44, Issue 1-3•September 2007, pp 97-113 • https://doi.org/10.1007/s10623-007-9068-3

Let $$\mathcal S$$ be a Desarguesian ( n --- 1)-spread of a hyperplane ý of PG ( rn , q ). Let and $${\bar B}$$ be, respectively, an ( n --- 2)-dimensional subspace of an element of $$\mathcal S $$ and a minimal blocking set of an (( r --- 1) n + 1)-...
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Small weight codewords in LDPC codes defined by (dual) classical generalized quadrangles
- Jon-Lark Kim
  Department of Mathematics, University of Louisville, 328 Natural Sciences Building, 40292, Louisville, KY, USA
  ,
- Keith E. Mellinger
  Department of Mathematics, University of Mary Washington, 1301 College Avenue, Trinkle Hall, 22401, Fredericksburg, VA, USA
  ,
- Leo Storme
  Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, 9000, Ghent, Belgium
Designs, Codes and Cryptography, Volume 42, Issue 1•Jan 2007, pp 73-92 • https://doi.org/10.1007/s10623-006-9017-6
Abstract
We find lower bounds on the minimum distance and characterize codewords of small weight in low-density parity check (LDPC) codes defined by (dual) classical generalized quadrangles. We analyze the geometry of the non-singular parabolic quadric in ...
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The classification of the smallest nontrivial blocking sets in PG(n, 2)
- Patrick Govaerts
  Department of Pure Mathematics and Computer Algebra, Ghent University, Gent, Belgium
  ,
- Leo Storme
  Department of Pure Mathematics and Computer Algebra, Ghent University, Gent, Belgium
Journal of Combinatorial Theory Series A, Volume 113, Issue 7•October 2006, pp 1543-1548 • https://doi.org/10.1016/j.jcta.2005.11.002

We determine the smallest nontrivial blocking sets with respect to t-spaces in PG(n, 2), n ≥ 3. For t = n - 1, they are skeletons of solids in PG(n, 2); for 1 ≤ t < n - 1, they are cones with vertex an (n - t - 3)- space π_{n-t - 3} and base the set of ...
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Q. What articles are eligible for ACM Author-Izer?
A. ACM Author-Izer can be applied to all the articles authors have ever published with ACM. It is also available to authors who will have articles published in ACM publications in the future.

Q. Are there any restrictions on authors to use this service?
A. No. An author does not need to subscribe to the ACM Digital Library nor even be a member of ACM.

Q. What are the requirements to use this service?
A. To access ACM Author-Izer, authors need to have a free ACM web account, must have an ACM Author Profile page in the Digital Library, and must take ownership of their Author Profile page.

Q. What is an ACM Author Profile Page?
A. The Author Profile Page initially collects all the professional information known about authors from the publications record as known by the ACM Digital Library. The Author Profile Page supplies a quick snapshot of an author's contribution to the field and some rudimentary measures of influence upon it. Over time, the contents of the Author Profile page may expand at the direction of the community. Please visit the ACM Author Profile documentation page for more background information on these pages.

Q. How do I find my Author Profile page and take ownership?
A. You will need to take the following steps:
- Create a free ACM Web Account
- Sign-In to the ACM Digital Library
- Find your Author Profile Page by searching the ACM Digital Library for your name
- Find the result you authored (where your author name is a clickable link)
- Click on your name to go to the Author Profile Page
- Click the "Add Personal Information" link on the Author Profile Page
- Wait for ACM review and approval; generally less than 24 hours

Q. Why does my photo not appear?
A. Make sure that the image you submit is in .jpg or .gif format and that the file name does not contain special characters

Q. What if I cannot find the Add Personal Information function on my author page?
A. The ACM account linked to your profile page is different than the one you are logged into. Please logout and login to the account associated with your Author Profile Page.

Q. What happens if an author changes the location of his bibliography or moves to a new institution?
A. Should authors change institutions or sites, they can utilize ACM Author-Izer to disable old links and re-authorize new links for free downloads from a new location.

Q. What happens if an author provides a URL that redirects to the author’s personal bibliography page?
A. The service will not provide a free download from the ACM Digital Library. Instead the person who uses that link will simply go to the Citation Page for that article in the ACM Digital Library where the article may be accessed under the usual subscription rules.

However, if the author provides the target page URL, any link that redirects to that target page will enable a free download from the Service.

Q. What happens if the author’s bibliography lives on a page with several aliases?
A. Only one alias will work, whichever one is registered as the page containing the author’s bibliography. ACM has no technical solution to this problem at this time.

Q. Why should authors use ACM Author-Izer?
A. ACM Author-Izer lets visitors to authors’ personal home pages download articles for no charge from the ACM Digital Library. It allows authors to dynamically display real-time download and citation statistics for each “authorized” article on their personal site.

Q. Does ACM Author-Izer provide benefits for authors?
A. Downloads of definitive articles via Author-Izer links on the authors’ personal web page are captured in official ACM statistics to more accurately reflect usage and impact measurements.

Authors who do not use ACM Author-Izer links will not have downloads from their local, personal bibliographies counted. They do, however, retain the existing right to post author-prepared preprint versions on their home pages or institutional repositories with DOI pointers to the definitive version permanently maintained in the ACM Digital Library.

Q. How does ACM Author-Izer benefit the computing community?
A. ACM Author-Izer expands the visibility and dissemination of the definitive version of ACM articles. It is based on ACM’s strong belief that the computing community should have the widest possible access to the definitive versions of scholarly literature. By linking authors’ personal bibliography with the ACM Digital Library, user confusion over article versioning should be reduced over time.

In making ACM Author-Izer a free service to both authors and visitors to their websites, ACM is emphasizing its continuing commitment to the interests of its authors and to the computing community in ways that are consistent with its existing subscription-based access model.

Q. How do authors access ACM Author-Izer?
A. See How to Use

Q. Why can’t I find my most recent publication in my ACM Author Profile Page?
A. There is a time delay between publication and the process which associates that publication with an Author Profile Page. Right now, that process usually takes 4-8 weeks.

Q. How does ACM Author-Izer expand ACM’s “Green Path” Access Policies?
A. ACM Author-Izer extends the rights and permissions that authors retain even after copyright transfer to ACM, which has been among the “greenest” publishers. ACM enables its author community to retain a wide range of rights related to copyright and reuse of materials. They include:
- Posting rights that ensure free access to their work outside the ACM Digital Library and print publications
- Rights to reuse any portion of their work in new works that they may create
- Copyright to artistic images in ACM’s graphics-oriented publications that authors may want to exploit in commercial contexts
- All patent rights, which remain with the original owner

Leo Storme

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Results

The characterisation of the smallest two fold blocking sets in PG(n, 2)

Theorems of Erdős-Ko-Rado type in polar spaces

Galois geometries and applications

In memoriam, András Gács

A study of (x(q + 1), x; 2, q)-minihypers

A spectrum result on maximal partial ovoids of the generalized quadrangle Q(4,q), q even

An empty interval in the spectrum of small weight codewords in the code from points and k-spaces of PG(n,q)

Generalised dual arcs and Veronesean surfaces, with applications to cryptography

Tight sets, weighted m-covers, weighted m-ovoids, and minihypers

Characterization results on arbitrary non-weighted minihypers and on linear codes meeting the Griesmer bound

On the code generated by the incidence matrix of points and hyperplanes in PG(n,q) and its dual

Partial ovoids and partial spreads in symplectic and orthogonal polar spaces

Partial ovoids and partial spreads in hermitian polar spaces

Small weight codewords in the codes arising from Desarguesian projective planes

On the smallest maximal partial ovoids and spreads of the generalized quadrangles W(q) and Q(4,q)

A weighted version of a result of Hamada on minihypers and on linear codes meeting the Griesmer bound

Characterization results on small blocking sets of the polar spaces Q+(2n + 1, 2) and Q+(2n + 1, 3)

Blocking Sets in PG(r, qn)

Small weight codewords in LDPC codes defined by (dual) classical generalized quadrangles

The classification of the smallest nontrivial blocking sets in PG(n, 2)