Publications

Regular papers

1. "On asymptotically good ramp secret sharing schemes," by O.Geil, S. Martin, U. Martínez-Peñ, R. Matsumoto. Published in Proceedings (electronic) of WCC-2015, edited by P. Charpin, 10 pages.
2. "Roots and coefficients of multivariate polynomials over finite fields," published in Finite Fields and their applications, Vol. 34, 2015, pp. 36.44 (arXiv).
3. "An improvement of the Feng-Rao bound for primary codes," by O. Geil and S. Martin. Published in Designs, Codes and Cryptography, Vol. 76 (1), 2015, pp. 49-79 (arXiv).
4. "Relative generalized Hamming weights of one-point algebraic geometric codes," by O. Geil, S. Martin, R. Matsumoto, D. Ruano and Y. Luo (arXiv). Published in IEEE Trans. Inform. Vol. 60, No. 10, 2014, pp. 5938--5949.
5. "Further improvements on the Feng-Rao bound for dual codes," by O. Geil and S. Martin (arXiv). Published in Finite Fields and Their Applications, Vol. 30, 2014, pp. 33--48.
6. "Affine variety codes are better than their reputation," by O. Geil and S. Martin. Published in Proceedings of the 21st Symposium on Mathematical Theory of Networkds and Systems, University of Groningen, 2014, pp. 137-141.
7. "Feng-Rao decoding of primary codes," by O. Geil, R. Matsumoto, and D. Ruano. Published in Finite Fields and their Applications, Vol. 23, 2013, pp. 35-52 (arXiv).
8. "Generalization of the Lee-O'Sullivan list decoding for one-point AG codes," by R. Matsumoto, D. Ruano, O. Geil. Published in Journal of Symbolic Computation, Volume 55, 2013, pp. 1-9 (arXiv).
9. "Weighted Reed-Muller codes revisited", by O. Geil and C. Thomsen. Published in Designs, Codes and Cryptography, Vol. 66, 2013, pp. 195-220 (arXiv).
10. "A new method for constructing small-bias spaces from Hermitian codes," by Olav Geil, Stefano Martin and Ryutaroh Matsumoto. Published in Proceedings of WAIFI-2012, Lecture Notes in Computer Science, LNCS 7369, pp. 29-44, 2012 (arXiv).
11. "Aspects of random network coding," by Olav Geil and Casper Thomsen. Published in "Algebraic Geometry Modeling in Information Theory," World Scientific (Series on Coding Theory and Cryptography), Edited by Edgar Martinez-Moro, pp. 47-81, 2013.
12. ``List Decoding Algorithms based on Groebner Bases for General One-Point AG Codes,'' by O. Geil, R. Matsumoto and D. Ruano. Published in Proc. 2012 IEEE International Symposium on Information Theory, July 1-6, 2012, Boston, MA, USA, 2012, pp. 86-90 (arXiv).
13. ``List decoding of a class of affine variety codes,'' by Olav Geil and Casper Thomsen. Published in Proceedings of WCC-2011, Paris, Ed. by D. Augot and A. Canteaut, 2011, pp. 263-272.
14. "On the order bounds for one-point AG codes," by Olav Geil, Carlos Munuera, Diego Ruano, and Fernando Torres. Published in Advances in Mathematics of Communications, 2011, pp. 489-504 (arXiv).
15. "Algebraic geometry codes from order domains," by Olav Geil. Published in Gröbner Bases, Coding, and Cryptography, Springer, 2009, Eds.: Sala, Mora, Perret, Sakata, Traverso, pp. 121-141 (pdf).
16. "Bounding the number of rational places using Weierstrass semigroups," by Olav Geil and Ryutaroh Matsumoto. Published in Journal of Pure and Applied Algebra, 213, (6), 2009, pp. 1152-1156 (Extended version can be found on arXiv).
17. "Evaluation Codes from an Affine Variety Code Perspective," by Olav Geil. Published in Advances in algebraic geometry codes, Ser. Coding Theory Cryptol., 5, World Sci. Publ., Hackensack, NJ, 2008, Eds.: E. Martinez-Moro, C. Munuera, D. Ruano, pp. 153-180 (pdf).
18. "On Field Size and Success Probability in Network Coding," by Olav Geil, Ryutaroh Matsumoto and Casper Thomsen. Published in Proc. of WAIFI-2008, Lecture Notes in Comput. Sci., Springer Verlag, 2008, pp. 157-173 (arXiv).
19. "On the second weight of generalized Reed-Muller codes," by Olav Geil. Published in Design, Codes and Cryptography, 2008, pp. 323-330 (pdf).
20. "Generalized Sudan's list decoding for order domain codes," by Olav Geil and R. Matsumoto. Published in Proc. of AAECC-17, Lecture Notes in Comput. Sci., LNCS 4851, Springer-Verlag, 2007, pp. 50-59 (pdf).
21. "Evaluation Codes from Order Domain Theory," by Henning E. Andersen and Olav Geil. Published in Finite Fields and Their Applications Vol. 14 (1), 2008, pp. 92-123 (pdf).
22. "On the Feng-Rao Bound for Generalized Hamming Weights," by Olav Geil and Christian Thommesen. Published in Proc. AAECC-16, Lecture Notes in Comput. Sci., Vol. LNCS 3857, Springer-Verlag, Berlin 2006, pp. 295-306 (pdf).
23. "On Codes from Norm-Trace Curves," by Olav Geil. Published in Finite Fields and Their Applications (9), 2003, pp. 351-371 (pdf).
24. "On the Structure of Order Domains," by Olav Geil and Ruud Pellikaan. Published in Finite Fields and Their Applications (8), 2002, pp. 369-396 (pdf).
25. "On Hyperbolic Codes," by Olav Geil and Tom Høholdt. Published in Proc. AAECC-14, LNCS 2227, Springer-Verlag, 2001, pp. 159-171.
26. "Footprints or Generalized Bezout's Theorem," by Olav Geil and Tom Høholdt. Published in IEEE Trans. on Inform. Theory, March 2000, pp. 635-641 (pdf).

Papers in preperation

• "Fulcrum network codes: a code for fluid allocation of complexity," by D. E. Lucani, M. V. Pedersne, D. Ruano, C. W. S&oring;rensen, F. H. P. Fitzek, J. Heide, O. Geil, submitted, 31 pages (pdf).
• "Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth's second tower," by O. Geil, S. Martin, U Martínez-Peñas, D. Ruano, submitted, 15 pages (pdf).
• "On asymptotically good ramp secret sharing schemes," by O.Geil, S. Martin, U. Martínez-Peñas, R. Matsumoto, submitted, 26 pages (pdf).
• "List Decoding Algorithm based on Voting in Groebner Bases for General One-Point AG Codes," by Olav Geil, Ryutaroh Matsumoto, Diego Ruano (arXiv). Submitted.
• "Relative generalized Hamming weights of q-ary Reed-Muller codes," by Stefano Martin and Olav Geil, 33 pages (arXiv), submitted.
• "More results on the number of zeros of multiplicity r," by Olav Geil and Casper Thomsen, 12 pages, submitted.

Miscellaneous

• "Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth's second tower," by O. Geil, S. Martin, U Martínez-Peñas, D. Ruano, in Proceedings of ACA 2015-Applications of Computer Algebra, Kalamata, Greece 2015, 5 pages
• (pdf)..
• "Combining subspace codes with classical linear error-correcting codes," by O. Geil, Louise Foshammer, and Malte Neve-Græsbøll, 6 pages, 2014.
• "A Note on the Injection Distance," by Stanislaw Bulygin, Olav Geil and Diego Ruano, 2010 (arXiv).
• "On the Number of Zeros of Multiplicity r," by Olav Geil and Casper Thomsen, 2009 (arXiv).
• Book Review of : Tracey Ho and Desmond S. Lun, Network Coding: An Introduction. Review published in: Computer Journal, 2009, (54), review by Olav Geil, p. 510 (pdf).
• ``Two applications of the footprint (or $\Delta$-set) bound : Estimation of generalized Hamming weights,'' by Olav Geil, poster at Special Semester on Gröbner Bases and Related Methods 2006, Workshop D1: Gröbner Bses in Cryptography, Coding Theory and Algebraic Combinatorics, Radon Institute for Computational and Applied Mathematics and Research Institute for Symbolic Computation, Linz, Austria, May 2006.
• ``On the minimum distance of one-point geometric Goppa codes,'' by Olav Geil and Henning E. Andersen in Proceedings of AGCT-10 : Arithmétique et Théorie de L'Information, CIRM, Luminy, Sept. 26-30 2005, Eds. Francois Rodier and Serge Vladut, Summary, 2 pages.
• Proceedings of the 8th Nordic Combinatorial Conference, edited by Lars Døvling Andersen and Olav Geil, Aalborg University 2004.
• "On some Gröbner Basis Theoretical Applications," by Olav Geil. Published in Proceedings of the 8th Nordic Combinatorial Conference, edited by Lars Døvling Andersen and Olav Geil, Aalborg University 2004, pp. 59-64.
• "The Missing Evaluation Codes from Order Domain Theory," by H. E. Andersen and O. Geil. Published in Proceedings of 2004 IEEE International Symposium on Information Theory, Chicago, p. 78.
• Book review of: Jørn Justesen & Tom Høholdt, A Course In Error-Correcting Codes. Review published in Matilde (newsletter for Dansk Matematisk Forening), 2004 ; nr. 21, review by Olav Geil and Christian Thommesen, p. 27.
• Book review of: Jørn Justesen & Tom Høholdt, A Course In Error-Correcting Codes. Review published in Newsletter of The European Mathematical Society, March 2005, review by Olav Geil and Christian Thommesen, pp. 39-40.
• "On Hyperbolic Type Codes," by O. Geil and T. Høholdt. Published in Proceedings of 2003 IEEE International Symposium on Information Theory, Yokohama, p. 331.
• "A Class of Groebner Basis Theoretically Based Evaluation Codes," by O. Geil, Published in Proceedings of 2002 IEEE International Symposium on Information Theory, Lausanne, p. 60.
• "Codes from Order Domains," by O. Geil. Published in Proceedings of 2001 IEEE International Symposium on Information Theory, Washington, 2001, p. 308.
• "Codes Based on an F_q-Algebra", by O. Geil. PhD-thesis Aalborg University, June 2000. ( part 0, part 1, part 2 ).