Iwan M. Duursma  -  Publications

      Last modified 01/16/2010

      Minimum distance bounds for AG codes:

• Interactive tables with bounds for the parameters of Hermitian, Suzuki and other codes from curves (maintained by Radoslav Kirov)
  
  
• 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)
  
  
• 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.
  
  
• Binomial moments for divisible self-dual codes [pdf], to appear.
  
  
• 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]
  
  
• 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)
  
  
• A group key agreement protocol from pairings, with Hyang-Sook Lee, Appl. Math. Comput. 167 (2005), no. 2, 1451--1456.
  
  
• Small weights in divisible codes, presented at Oberwolfach, December 2003, full paper in preperation. [.pdf] (version AMS/SMM - Houston: [.pdf])
  
  
• 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.
  
  
• Combinatorics of the two-variable zeta function, Finite fields and applications, 109--136, Lecture Notes in Comput. Sci., 2948, Springer, Berlin, 2004 [.ps]
  
  
• 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]
  
  
• 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]
  
  
• Computing Symmetrized Weight Enumerators for Lifted Quadratic Residue Codes, with Greferath, M., Submitted. [.ps]
  
  
• 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]
  
  
• 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]
  
  
• Extremal weight enumerators and ultraspherical polynomials, Discrete Mathematics, vol. 268, no. 1-3, pp. 103-127, July 2003. [.ps]
  
  
• 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]
  
  
• Twisted Klein curves modulo 2, [.ps]
  
  
• 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]
  
  
• From weight enumerators to zeta functions, Discrete Applied Mathematics, vol. 111, no. 1-2, pp. 55-73, 2001. [.ps]
  
  
• Reed-Muller codes on complete intersections, with Renteria, C. and Tapia-Recillas, H., AAECC, vol. 11, pp. 455-462, 2001. [.ps]
  
  
• Preparata codes through lattices, IEEE Trans. on Inform. Theory, vol. 47, pp. 36-44, January 2001. [.ps]
  
  
• 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]
  
  
• 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.
  
  
• 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]
  
  
• Monomial embeddings of the Klein curve, Discrete Mathematics, Guest-Ed. G. Faina, vol.208/209, pp.235-246, October 1999. [.ps]
  
  
• Weight distributions of geometric Goppa codes, Transactions of the AMS, vol. 351, pp. 3609-3639, September 1999. [.ps]
  
  
• Hyperelliptic cryptosystems from curves y² = x^p-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]
  
  
• 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.
  
  
• 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.
  
  
• Class numbers for some hyperelliptic curves, In: "Arithmetic, Geometry and Coding Theory," eds. Pellikaan, Perret, Vladuts, pp.45-52, publ. deGruyter, Berlin, 1996. [.ps]
  
  
• Error-locating pairs for cyclic codes, with Koetter, R., IEEE Trans. on Inform. Theory, vol. 40, pp. 1108-1121, July 1994. [.ps], [.pdf]
  
• Majority coset decoding, IEEE Trans. on Inform. Theory, vol. 39, pp. 1067-1070, 1993.
  
  
• On the decoding procedure of Feng and Rao, Proceedings Algebraic and Combinatorial Coding Theory III,
  Voneshta Voda, Bulgaria, pp.64-67, June 1992.
  
  
• Algebraic decoding using special divisors, IEEE Trans. on Inform. Theory, vol. 39, pp. 694-698, 1993.
  
  

• 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.
  
  
• 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.
  
  
• 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.
  
  
• On termination criteria for decoding algorithms, Proceedings EIDMA Winter Meeting,
  Veldhoven, The Netherlands, 2 pages, December 1994.
  
  
• Average weight distributions for AG-codes,
  Proceedings Algebraic and Combinatorial Coding Theory IV,
  Novgorod, Russia, September 1994.
  
  
• On erasure decoding of AG-codes,
  Proceedings IEEE Information Theory Workshop,
  Moscow, Russia, 7 pages, July 1994. [.pdf]
  
  
• 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)
  
  

• 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]