Publications of Klaus Metsch

submitted or accepted papers

With J. De Beule, A. Hallez and L. Storme: Sets of generators blocking all generators in finite classical polar spaces. Preprint
With Th. Meixner: Von einer Extremwertaufgabe zur Inversion am Kreis, Submitted to th. Semesterberichte.
With Nora V. Harrach: Small point sets of PG(n,q^3) intersecting each k-subspace in 1 mod q points, Designs, Codes and Cryptography, submitted
With Nora V. Harrach, Tamas Szönyi and Zsuzsa Weiner: Small point sets of PG(n,p^(3h)) intersecting each line in 1 mod p^h points, J. of Geometry, submitted
With Th. Meixner: Über Schwerpunkte von Vierecken II, Preprint.
With Th. Meixner: Über Schwerpunkte von Vierecken I, Preprint.
With A. Klein and L. Storme: Small maximal partial spreads in classical finite polar spaces, Advances in Geometry, to appear.
The number of lines needed to block all planes in PG(5,q), Quaderni di matematica, to appear.

2008

With A. Klein: On Approximate Inclusion-Exclusion, Innovations in Incidence Geometry 6-7 (2007-2008), 249-270.
With J. De Beule, A. Klein and L. Storme: Partial ovoids and partial spreads of classical finite polar spaces, Serdica Mathematical Journal 34 (2008) , 689-714.
With L. Storme: Tangency sets in PG(3,q). JCD 16 (no. 6) (2008), 462-476.
With J. De Beule and L. Storme: Characterization results on arbitrary non-weighted minihypers and on linear codes meeting the Griesmer bound Designs, Codes and Cryptography 49 (2008), 187-197
With J. De Beule and L. Storme: Characterization results on weighted minihypers and on linear codes meeting the Griesmer bound Advances in Mathematics of Communications 2 (2008), 261-272
With J. De Beule, A. Klein and L. Storme: Partial ovoids and partial spreads in hermitian polar spaces. Designs, Codes and Cryptography. 47 (2008), 21-34.
With J. De Beule, A. Klein and L. Storme: Partial ovoids and partial spreads in symplectic and orthogonal polar spaces. Europ. J. Combinatorics 29 (2008), 1280-1297
With L. Storme: Maximal partial ovoids and maximal partial spreads in hermitian generalized quadrangles. JCD 16 (2008), 101-116

2007

With J. De Beule: The maximum size of a partial spread in H(5,q²) is q³+1. Journal of Combinatorial Theory, Series A , 114 (2007), 761-768.
With A. Klein: Parameters for which the Griesmer bound is not sharp, Discrete Math.307 (2007), 2695-2703
With J. De Beule, and L. Storme: Characterization results on small blocking sets of the polar spaces Q⁺(2n+1,2) and Q⁺(2n+1,3). Designs, Codes and Cryptography 44 (2007), 197-207

2006

How many s-subspaces must miss a point set in PG(n,q), J. Geom. 86 (2006), 154-164
Small maximal partial ovoids of H(3,q²), Innovations in Incidence Geometry, 3 (2006), 1-12.
How many lines must miss d points in a linear space, Journal of Combinatorial Design 14 (2006), 441-450.

2005

With J. De Beule: The Hermitian variety H(5,4) has no ovoid. Bull. Belg. Math. Soc. 12 (2005), 727-733.
With A. Klein: New results on covers and partial spreads of polar spaces, Innovations in Incidence Geometry 1 (2005), 19-34.
Blocking structures of of hermitian varieties, Designs, Codes and Cryptography 34 (2005), 339-360.
With J. De Beule: The smallest point sets that meet all generators of H(2n,q²). Discrete Math. 294 (2005), 75-81
With J. De Beule: Minimal blocking sets of size q²+2 of Q(4,q), q an odd prime, do not exist. Finite Fields and Applications 11 (2005), 305-315.

2004

Blocking subspaces by lines in PG(n,q), Combinatorica 24 (2004), 459-486.
with Th. Meixner: Bestimmung aller Vierecke, in den Flächen- und Kantenschwerpunkt zusammenfallen, Math. Semesterber. 51 (2004), 131-145.
With J. De Beule: Small point sets that meet all generators of Q(2n,p), p>3 prime, JCT (A) 106 (2004), 327-333.
Small point sets that meet all generators of W(2n+1,q). Designs, Codes and Cryptography 31 (2004), 283-288.

2003

On the size of maximal caps in Q⁺(5,q), Advances in Geometry, Special Issue (2003), 186-205.
A Bose-Burton Type theorem for quadrics, J. Combin. Des. 11 (2003), 317-338.
On the characterization of the folded halved cubes of small diameter by their parameters, Designs, Codes and Cryptography 29 (2003), 215-225.
Blocking sets in projective spaces and polar spaces, J. Geom. 76 (2003), 216-232.

2002

With L. Storme: Partial linear complexes in PG(3,q), Discrete Math. 255 (2002), 287-296.
With M. Bokler: On the smallest minimal blocking sets in projective space generating the whole space, Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry 43 (2002), 43-53.

2000

With L. Storme: 2-Blocking Sets in PG(4,q), q Square, Beiträge zur Algebra und Geometrie (Contributions to Algebra and Geometry) 41 (2000), 247-255.
On blocking sets of quadrics. J. Geom. 67 (2000), 188-207.

1999

With L. Storme: Partial t-spreads in PG(2t+1,q). Designs, Codes and Cryptography 18 (1999), 199-216.
Bose-Burton Type Theorems for Finite Projective, Affine and Polar Spaces. London mathematical Society, Lecture Notes Series 267 (1999), 137-166.
A Bose-Burton Theorem for Elliptic Polar Spaces. Designs, Codes and Crytography 17 (1999), 219-224.
With G. Ebert and T. Szönyi: Caps Embedded in Grassmannian Surfaces. J. Geom. 70 (1999), 181-196.
With P. De Vito, E. Ferrara Dentice, P.M. Lo Re: Embedding the planar structure of 4-dimensional linear spaces into projective spaces. J. Geom. 64 (1999), 67-79.
On a Characterization of Bilinear Froms Graphs. Europ. J. Combinatorics 20 (1999), 293-306.
With B. Webb: A note on the Cycle Structures of Automorphisms of 2-(v,k,1)-Designs. Ars Comb. 51 (1999), 224-228.

1998

The sets closest to ovoids in O^-(2n+1,q). Bull. Belg. Math. Soc. 5 (1998), 389-392.

1997

Characterization of the folded Johnson graphs of small diameter by their intersection array. Europ. J. Combinatorics 18 (1997), 901-913.
A note on Buekenhout-Metz Unitals, pp. 177-180 in {\it Geometry, Combinatorial Design and Related Structures} (ed. J.W.P. Hirschfeld, S.S. Magliaveras and M.J. de Resmini), London Math. Soc. Lecture Notes 49, Cambridge University Press, Cambridge 1997.
Embedding theorems for locally projective three-dimensional linear spaces. Discrete Math. 174 (1997), 227-245.
On the characterization of the folded Johnson graphs and the folded halved cubes by their intersection array. Europ. J. Combinatorics 18 (1997), 65-74.
Embedding the linear structure of planar spaces into projective spaces. Designs, Codes and Cryptography 10 (1997), 251-263.
With J. Eisfeld: Blocking s-dimensional subspaces by lines in PG(2s,q). Combinatorica 17 (1997), 151-162.

1996

On the number of lines of 4-dimensional linear spaces. J. Geom. 56 (1996), 102-112.
With N. Durante: A characterization of projective 3-spaces. J. Comb. Designs 5 (1996), 377-387.

1995

A remark on the uniqueness of embeddings of linear spaces into desarguesian projective planes. J. Comb. Design. 3 (1995), 293-297.
On the number of lines in planar spaces. Combinatorica 15 (1995), 105-110.
A characterization of Grassmann graphs. Europ. J. Combinatorics 16 (1995), 171-195.
Twisted Derivations and and distinct sets of lines that cover the same pairs of points. Geometriae Dedicata 54 (1995), 171-197.
The Theorem of Totten for planar spaces. Rendiconti di Matematica 15 (1995), Serie VII, 211-232.
Quasi-residual designs, 1½-designs and strongly regular multigraphs. Discrete Mathematics 143 (1995), 167-188.

1994

Classification of non-embeddable partial planes with the maximum possible number of lines. Atti Sem. Mat. Fis. Univ. Modena XLII (1994), 19-35.

1993

With A. Blokhuis: Large minimal blocking sets, strong representative systems and partial unitals. Proceedings der zweiten Deinze-Konferenz (Finite Geometries and Combinatorics, Cambridge University Press 1993, Ed. F. De Clerck et al.), pp. 37-52.
With A. Blokhuis, G.E. Moorhouse, R. Ahlswede and S.L. Bezrukov: Partioning the n-cube into Sets with Mutual Distance 1. Appl. Math. Lett. Vol 6, No. 4 (1993), 17-19 .
With A. Blokhuis: On the size of a maximal partial spread. Designs, Codes and Cryptography 3 (1993), 187-191.
Proof of the Dowling-Wilson Conjecture. Bull. Math. Soc. Belg. 45 (1993), Ser. B, 69-98.

1992

On the maximum size of a maximal partial plane. Rendiconti di Matematica (VII) 12 (1992), 345-355.
Linear spaces with n²+n+2 lines. Europ. J. Combinatorics 13 (1992), 503-513.
Linear spaces with few lines. Discrete Mathematics 110 (1992), 215-222.
Linear Spaces in which every line of maximal degree meets only few lines. Proceedings of the Conferences on Combinatorics, Gaeta, Italy, 20-27 May, 1990, pp. 391-402. Elsevier Science Publisher 1992.

1991

Improvement of Bruck's Completion Theorem. Designs, Codes and Cryptography 1 (1991), 99-116.
With P. De Vito und P.M. Lo Re: Linear spaces in which every long line intersects v+2 other lines. Arch. Math. 57 (1991), 193-203.
Blocking sets in PG(3,4)? Mitt. Math. Sem. Giessen 210 (1991), 119-131.

1990

On the existence of certain (7,1)-designs. J. of Combinatorics, Information and System Science 15 (1990), 70-84.
With A. Blokhuis, A.R. Calderbank and A.Seress. An embedding theorem for partial linear spaces with applications to coding theory. Proceedings of the Isle of Thorns Conference 1990 (Advances in Finite Geometries and Designs, Oxford Science Publications, Ed. J.W.P. Hirschfeld, D.R. Hughes and J.A. Thas), S. 35-46.
With R. Mullin, B. Gardner and G.H.J. van Rees: Some Properties of Finite Bases for the Rosa Set. Utilitas Math. 38 (1990), 199-215.
Classification of linear spaces without three mutually parallel lines. J. Geom. 37 (1990), 128-141.

1989

Embedding Finite Planar Spaces into 3-Dimensional Projective Spaces. J. of Comb. Theory A (1989), 161-168.
Extending the complement of the union of disjoint Baer-subplanes to a projective plane. Proceedings of the International Conference on Incidence Geometries and Combinatorial Structures held in Ravello, 1988, (Research and Lecture Notes in Mathematics, Mediterranean Press, Ed. A. Barlotti et al.), 2nd volume, pp. 243-251.

1988

An improved bound for the embedding of linear spaces into projective planes. Geometriae Dedicata 26 (1988), 333-340.
An optimal bound for embedding linear spaces into projective planes. Discrete Math. 70 (1988), 53-70.
Embedding locally projective planar spaces into projective spaces. Annals of Discrete Math. 37 (1988), 293-296.

1987

With A. Beutelspacher: Embedding finite linear spaces in projective planes II. Discrete Math. 66 (1987), 219-230.

1986

With A. Beutelspacher: Embedding finite linear spaces in projective planes. Annals of Discrete Math. 30 (1986), 39-56.