Publications
Last modified 01/16/2010 (page no longer updated, use pub2012)
Minimum distance bounds for AG codes:
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Interactive tables with bounds for the parameters of Hermitian, Suzuki and other codes
from curves (maintained by Radoslav Kirov)
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Selected presentations:
Linear programming for secret sharing thresholds [pdf] (AMS meeting, Bllomington, April 6, 2008)
AG codes defined by divisors with base points [pdf] (AGCT-12, Luminy, April 1, 2009)
An extension of the order bound for AG codes [pdf]
(AAECC-18, Tarragona, June 9, 2009)
Codes from planes and curves, part 1 [pdf] part 2 [slideshow] (AAECC-18, Tarragona, June 10, 2009)
Lower bounds on distances of improved two-point codes [pdf] (Finite Fields and Applications, Dublin, July 21, 2009)
Distance bounds for AG codes [pdf] (Worksop on sequences, codes and curves, Antalya, September 28, 2009)
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Selected publications:
Algebraic geometry codes: general theory, 48 pages, June 2008,
[.pdf] (Erratum)
Minimum distance of Hermitian two-point codes, by Seungook Park, 21 pages, February 2009
[arXiv]
Coset bounds for algebraic geometric codes, with Seungkook Park, 36 pages, October 2008
[arXiv]
Submitted in two parts: Coset bounds for algebraic geometric codes [pdf],
to appear FFA,
Delta sets for divisors supported in two points[pdf]
An extension of the order bound for AG codes, with Radoslav Kirov, 11 pages, January 2009, in: Proceedings AAECC-18.
[arXiv]
Distance bounds for algebraic geometric codes, with Radoslav Kirov and Seungkook Park, January 2010.
[arXiv]
- Two-point coordinate rings for GK-curves , submitted.
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Binomial moments for divisible self-dual codes [pdf], to appear.
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A symmetric Roos bound for linear Codes, with Ruud Pellikaan, J. Combin. Theory Ser. A 113 (2006), no. 8, 1677--1688. (special issue in honor of Jack van Lint)
[.pdf]
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The Vector Decomposition Problem for Elliptic and Hyperelliptic Curves, with Negar Kiyavash,
J. Ramanujan Math. Soc. 20 (2005), no. 1, 59--76.
[.pdf] [.ps]
(scanned version in pdf of the paper [Yos03] by Yoshida)
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A group key agreement protocol from pairings, with Hyang-Sook Lee,
Appl. Math. Comput. 167 (2005), no. 2, 1451--1456.
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Small weights in divisible codes, presented at Oberwolfach, December 2003,
full paper in preperation. [.pdf]
(version AMS/SMM - Houston: [.pdf])
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Everywhere ramified towers of global function fields, with Bjorn Poonen and Michael Zieve,
Finite fields and applications, 148--153, Lecture Notes in Comput. Sci., 2948, Springer, Berlin, 2004.
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Combinatorics of the two-variable zeta function,
Finite fields and applications, 109--136, Lecture Notes in Comput. Sci., 2948, Springer, Berlin, 2004
[.ps]
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Tate-pairing implementations for tripartite key agreement, with Hyang-Sook Lee,
Advances in cryptology---ASIACRYPT 2003, 111--123, Lecture Notes in Comput. Sci., 2894,
Springer, Berlin, 2003.
[.ps]
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Results on zeta functions for codes,
Fifth Conference on Algebraic Geometry, Number Theory, Coding Theory and Cryptography, University of Tokyo,
January 17-19, 2003. [.ps]
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Computing Symmetrized Weight Enumerators for Lifted Quadratic Residue Codes, with Greferath, M.,
Submitted. [.ps]
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Geometric Reed-Solomon codes of length 64 and 65 over F8,
with Chien-Yu Chen, IEEE Trans. on Inform. Theory, vol. 49, pp. 1351-1353, May 2003.
[.ps]
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Bounds for completely decomposable Jacobians, with Enjalbert, J.-Y.,
Finite fields with applications to coding theory, cryptography and related areas (Oaxaca, 2001), 86--93,
Springer, Berlin, 2002.
[.ps]
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Extremal weight enumerators and ultraspherical polynomials,
Discrete Mathematics, vol. 268, no. 1-3, pp. 103-127, July 2003.
[.ps]
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A Z8 linear lift of the binary golay code and a non-linear binary (96,237,24) code,
with Greferath, M., Litsyn, S.N., and Schmidt, S.E.,
IEEE Trans. on Inform. Theory, vol. 47, pp. 1596-1598, May 2001.
[.ps]
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Twisted Klein curves modulo 2,
[.ps]
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A Riemann hypothesis analogue for self-dual codes,
In: Codes and Association schemes, Eds. Barg and Litsyn, AMS Dimacs Series, vol. 56, pp. 115-124, 2001.
[.ps]
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From weight enumerators to zeta functions,
Discrete Applied Mathematics, vol. 111, no. 1-2, pp. 55-73, 2001.
[.ps]
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Reed-Muller codes on complete intersections, with Renteria, C. and Tapia-Recillas, H.,
AAECC, vol. 11, pp. 455-462, 2001. [.ps]
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Preparata codes through lattices,
IEEE Trans. on Inform. Theory, vol. 47, pp. 36-44, January 2001.
[.ps]
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On the optimal Z4 codes of type II and length 16 ,
with Greferath, M. and Schmidt, S.E., J. of Comb. Th. Ser. A, vol. 92, pp. 77-82, 2000.
[.ps]
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Speeding up the discrete log computation on curves with automorphisms, with Gaudry, P., and Morain, F.,
Advances in Cryptology - ASIACRYPT '99, Kwok Yan Lam, Eiji Okamoto, Chaoping
Xing, Eds.,
Springer LNCS 1716, pp.103-121, November 1999.
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Split weight enumerators for the Preparata codes with applications to designs,
with Helleseth, T., Rong, C. and Yang, K., Designs, Codes and Cryptography, vol. 18, pp. 103-124, December 1999.
[.ps]
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Monomial embeddings of the Klein curve,
Discrete Mathematics, Guest-Ed. G. Faina, vol.208/209, pp.235-246, October 1999.
[.ps]
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Weight distributions of geometric Goppa codes,
Transactions of the AMS, vol. 351, pp. 3609-3639, September 1999. [.ps]
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Hyperelliptic cryptosystems from curves y2 = xp-x+1 over finite fields
of odd characteristic p, with Sakurai K.,
in: Coding theory, cryptography and related areas (Guanajuato, 1998), 73--89, Springer, Berlin, 2000.
[.ps]
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Cyclic subcodes of generalized Reed-Muller codes, with Cherdieu, J-P., Edouard, A. and Moreno, O.,
IEEE Trans. on Inform. Theory, vol. 44, pp. 307-311, January 1998.
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Translates of Z4-linear codes, with Bonnecaze, A.,
IEEE Trans. on Inform. Theory, vol. 43, pp. 1218-1230, July 1997.
[.ps]
- Generalized Hamming weights for duals of BCH codes, and maximal algebraic function fields,
with Stichtenoth, H. and Voss, C.,
In: "Arithmetic, Geometry and Coding Theory,"
eds. Pellikaan, Perret, Vladuts, pp.53-65, publ. deGruyter, Berlin, 1996.
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Class numbers for some hyperelliptic curves,
In: "Arithmetic, Geometry and Coding Theory,"
eds. Pellikaan, Perret, Vladuts, pp.45-52, publ. deGruyter, Berlin, 1996.
[.ps]
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Error-locating pairs for cyclic codes, with Koetter, R.,
IEEE Trans. on Inform. Theory, vol. 40, pp. 1108-1121, July 1994.
[.ps], [.pdf]
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Majority coset decoding,
IEEE Trans. on Inform. Theory, vol. 39, pp. 1067-1070, 1993.
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On the decoding procedure of Feng and Rao,
Proceedings Algebraic and Combinatorial Coding Theory III,
Voneshta Voda, Bulgaria, pp.64-67, June 1992.
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Algebraic decoding using special divisors,
IEEE Trans. on Inform. Theory, vol. 39, pp. 694-698, 1993.
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From weight enumerators to zeta functions,
Thirty-Seventh Annual Allerton Conference on Communication, Control, and
Computing,
Monticello, Illinois, USA, September 1999. (Short version of journal article)
- Interpolation and approximation in decoding,
Proceedings IEEE Information Theory Workshop,
Killarney, Ireland, 1 page, June 1998.
- Quadratic residue codes and hyperelliptic curves,
Thirty-Fifth Annual Allerton Conference on Communication, Control, and
Computing,
Monticello, Illinois, USA, pp.41-43, October 1997.
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Lattices and codes over rings, with Boutros, J.,
Thirty-Fourth Annual Allerton Conference on Communication, Control, and Computing,
Monticello, Illinois, USA, pp.322-324, October 1996.
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The association scheme for the Preparata codes, with Bonnecaze, A.,
Thirty-Third Annual Allerton Conference on Communication, Control, and Computing,
Monticello, Illinois, USA, pp.908-910, October 1995.
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On termination criteria for decoding algorithms,
Proceedings EIDMA Winter Meeting,
Veldhoven, The Netherlands, 2 pages, December 1994.
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Average weight distributions for AG-codes,
Proceedings Algebraic and Combinatorial Coding Theory IV,
Novgorod, Russia, September 1994.
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On erasure decoding of AG-codes,
Proceedings IEEE Information Theory Workshop,
Moscow, Russia, 7 pages, July 1994.
[.pdf]
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Error-locating pairs for cyclic codes, with Koetter, R.,
Proceedings Joint Russian-Swedish Workshop on Information Theory VI,
M"olle, Sweden, pp.123-127, August 1993. (Short version of journal article)
- Partition designs on divisor class groups and weight distributions,
Proceedings Joint Russian-Swedish Workshop on Information Theory VI,
M"olle, Sweden, pp.128-131, August 1993.
Other
- [65,13,36] code modulo 5, [Magma]
Brouwer Tables
- self-dual [32,16,11] over F4, [Magma] Brouwer Tables Gaborit Tables (self-dual codes)
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Duursma, I. M., Distribution des r‰sidues quadratiques,
Seminar March 16, 2000. [.ps]
- Duursma, I. M., and Tolhuizen, L., Fouten verbeterende codes, 10 pages,
Chapter in: "Kaleidoscoop 2," (Dutch), Eds.: B. de Smit and J. Top,
publ. Epsilon, The Netherlands, 1998.
- Duursma, I. M., Geometric Goppa codes, 12 pages,
Chapter in: "Error-correcting codes: a first course," H. van Tilborg,
Lund Studentlitteratur, 1993.
- Duursma, I. M., Decoding codes from curves and cyclic codes,
Thesis, Technical University Eindhoven, xiv+98 pages, September 1993.
Advisors: J. H. van Lint and H. Stichtenoth (University of Essen), Coadvisor: G. R.
Pellikaan. [.ps] [.pdf] titlepage and stellingen
- Duursma, I.M., Some remarks on Goppa codes,
Master's thesis, Universiteit van Amsterdam, Advisor: G. van der Geer, February 1989.
(Maximal Fermat curves pdf,
A large Fermat code pdf,
Locator algorithm, MacWilliams pdf)
Unpublished
- Duursma, I.M., Zeta functions for linear codes, 12 pages, July 1997.
- Duursma, I. M., Twisted Klein curves in even characteristic, 5 pages,
March 1996.
- Duursma, I. M., The geometry of the flexpoints of the Klein curve, 6 pages,
May 1995.
- Duursma, I. M., Decoding linear codes, Preprint CNRS UPR-9016
[.pdf] (also [.pdf])
Luminy, France, 10 pages, April 1994.
- Duursma, I. M., Additive problems over finite abelian groups, 13 pages,
March 1994.
- Duursma, I. M., Weight enumerators for codes from the Klein quartic, 5 pages,
November 1993.
[ps]