Preprints, slides and drafts

Schubert Unions in Grassmann Varieties

Authors: Johan P. Hansen, Trygve Johnsen, Kristian Ranestad
Comments: 37 pages, 2 figures
Subj-class: Algebraic Geometry; Combinatorics
MSC-class: 14M15 (05E15, 94B27)
Presented at arXiv, 7. 3. 2005: arXix
We study subsets of Grassmann varieties G(l,m) over a field F, such that these subsets are unions of Schubert cycles, with respect to a fixed flag. We study the linear spans of, and in case of positive characteristic, the number of points on such unions over finite fields. Moreover we study a geometric duality of such unions, and give a combinatorial interpretation of this duality. We discuss the maximum number of points over a finite field for the Schubert unions of a given spanning dimension, and we give some applications to coding theory. We define Schubert union codes, and study the parameters and support weights of these codes and of the well-known Grassmann codes.

Toric surfaces and codes, techniques and examples.

Talk and slides presented at IV International Algebraic Conference in Ukraine, Lviv, august 2003, pdf
Manuscript submitted for publication pdf

Fejlkorrigerende � koder, Toriske varieteter og Hirzebruch flader Slides for talk at Norsk kryptoseminar, Trondhjem, Norge, okt. 2002 pdf

Dependent rational points on curves over finite fields - Lefschetz theorems and exponential sums. ps. Slides for talk at the confererece Fq6, Mexico, may 2001.

Dependent rational points on curves over finite fields - Lefschetz theorems and exponential sums

Published in Electronic Notes in Discrete Mathematics, Elsevier Science. Volume 6 (2001)
[Abstract] [Full text] (PostScript 166.6 Kb) [BibTeX]
Presented at WCC Paris, International Workshop on Coding and Crypthography, jan. 2001.
Published in Proceedings of the International Workshop on Coding and Cryptography, 8-12 Janvier 2001, Paris (France). Editors Daniel Augot and Claude Carlet. 265-278. ps, pdf

Toric Varieties Hirzebruch Surfaces and Error-Correcting Codes.
Published in Applicable Algebra in Engineering, Communication and Computing, Springer Verlag, Volume 13, Issue 4 (2002), pp 289-300. Springer Link, pdf

Lower Bounds for Dynamic Algebraic Problems.
Joint with Gudmund Skovbjerg Frandsen and Peter Bro Miltersen

Presented STACS 99
Published (in shortened version) in LNCS 1563, p. 362 ff. Abstract | Full article in PDF (189 KB)
Published in Information and Computation, Academic Press. 171 (2001), 2, 333-349, ps.

On Lefschetz theorems and dependent rational points. Preprint pdf. Joint paper with Gilles Lachaud, IML, Marseille.

Linkage and Codes on Complete Intersections. Preprint pdf. Published in Applicable Algebra in Engineering, Communication and Computing, Springer Verlag, Springer-Verlag Heidelberg , Volume 14, Number 3, 2003, 175 - 185. Springer Link

On toric Varieties and Codes. pdf. Presented at 1998 Information Theory Workshop, Killarney, Ireland. Published in Proceedings of 1998 Information Theory Workshop, Killarney, Ireland. IEEE Catalog Number 98EX131. IEEE Xplore

Toric surfaces and error-correcting codes

Presented at the International Conference on Coding Theory, Cryptography and Related Areas, held in Guanajuato, in April 1998
Published in Coding Theory, Cryptography and Related Areas. Proceedings of an International Conference on Coding Theory, Cryptography and Related Areas, held in Guanajuato, in April 1998, 132--142, Springer, Berlin, 2000.