Publications

Last modified 03/17/2013, for downloadable preprints arXiv or here, mathscinet, bibtex

   Thesis

Duursma, I., Decoding codes from curves and cyclic codes, 1993, xiv+96 pages. Advisor Jack van Lint.

   Book Chapters

Duursma, I., Geometric Goppa codes, in: Error-correcting codes: a first course, H. van Tilborg, Lund Studentlitteratur, 1993.
Duursma, I. and Tolhuizen, L., Codetheorie voor CD-spelers, in: Speeltuin van de wiskunde, pp. 45-55, Veen Magazines, Diemen, Netherlands, 2003.
Duursma, I., Algebraic geometry codes: general theory, in: Advances in algebraic geometry codes, pages 1-48, Series on Coding Theory and Cryptology, 5, World Scientific Publishing Co., Hackensack, NJ, 2008.

   Journals

Duursma, I., Algebraic decoding using special divisors, IEEE Transactions on Information Theory, vol. 39, no. 2, pp. 694-698, 1993.
Duursma, I., Majority coset decoding, IEEE Transactions on Information Theory, vol. 39, no. 3, pp. 1067-1070, 1993.
Duursma, I. and Koetter, R., Error-locating pairs for cyclic codes, IEEE Transactions on Information Theory, vol. 40, no. 4, pp. 1108-1121, 1994.
Bonnecaze, A. and Duursma, I., Translates of linear codes over $Z_4$, IEEE Transactions on Information Theory, vol. 43, no. 4, pp. 1218-1230, 1997.
Cherdieu, J.-P., Duursma, I., Edouard, A., and Moreno, O., Cyclic subcodes of generalized Reed-Muller codes, IEEE Transactions on Information Theory, vol. 44, no. 1, pp. 307-311, 1998.


Duursma, I., Weight distributions of geometric Goppa codes, Transactions of the AMS, vol. 351, no. 9, pp. 3609-3639, 1999.
Duursma, I., Monomial embeddings of the Klein curve, Discrete Mathematics, Guest-Ed. G. Faina, vol. 208/209, pp. 235-246, 1999.
Duursma, I., Helleseth, T., Rong, C., and Yang, K., Split weight enumerators for the Preparata codes with applications to designs, Designs, Codes and Cryptography, vol. 18, no. 1-3, pp. 103-124, 1999.
Duursma, I., Greferath, M., and Schmidt, S.E., On the optimal $Z_4$ codes of type II and length 16, Journal of Combinatorial Theory Series A, vol. 92, no. 1, pp. 77-82, 2000.
Duursma, I., Preparata codes through lattices, IEEE Transactions on Information Theory, vol. 47, no. 1, pp. 36-44, 2001.


Duursma, I., Renteria, C., and Tapia-Recillas, H., Reed-Muller codes on complete intersections, Applicable Algebra in Engineering, Communication and Computing (AAECC Journal), vol. 11, no. 6, pp. 455-462, 2001.
Duursma, I., From weight enumerators to zeta functions, Discrete Applied Mathematics, vol. 111, no. 1-2, pp. 55-73, 2001.
Duursma, I., Greferath, M., Litsyn, S.N., and Schmidt, S.E., A ${\mathbb Z}_8$-linear lift of the binary Golay code and a nonlinear binary $(96,2^{37},24)$-code, IEEE Transactions on Information Theory, vol. 47, no. 4, pp. 1596-1598, 2001.
Duursma, I., Extremal weight enumerators and ultraspherical polynomials. Discrete Mathematics, vol. 268, no. 1-3, pp. 103-127, 2003.
Chen, C.-Y. and Duursma, I., Geometric Reed-Solomon codes of length 64 and 65 over $\mathbb F_8$, IEEE Transactions on Information Theory, vol. 49, no. 5, pp. 1351-1353, 2003.


Duursma, I. and Lee, H.-S., A group key agreement protocol from pairings, Applied Mathematics and Computation, vol. 167, no. 2, pp. 1451-1456, 2005
Duursma, I. and Kiyavash, N., The vector decomposition problem for elliptic and hyperelliptic curves, Journal of the Ramanujan Mathematical Society, vol. 20, no. 1, pp. 59-76, 2005.
Duursma, I. and Pellikaan, R., A symmetric Roos bound for linear codes, Journal of Combinatorial Theory Series A, vol. 113, no. 8, pp. 1677-1688, 2006.
Duursma, I. and Park, S., Coset bounds for algebraic geometric codes, Finite Fields and Their Applications, vol. 16, no. 1, pp. 36-55, 2010.
Duursma, I., Binomial moments for divisible self-dual codes, International Journal of Information and Coding Theory, in Honour of the Retirement of Vera Pless, vol. 1, no. 2, pp. 191-199, 2010.


Duursma, I., Kirov, R., Park, S., Distance bounds for algebraic geometric codes, J. Pure Appl. Algebra, vol. 215, no. 8, pp. 1863-1878, 2011.
Duursma, I., Two-point coordinate rings for GK-curves, IEEE Trans. Inform. Theory, vol. 57, no. 2, pp. 593-600, 2011.
Duursma, I., Kirov R., Improved two-point codes on Hermitian curves. IEEE Trans. Inform. Theoryvol. 57, no. 7, pp. 4469-4476, 2011.
Duursma, I., Park, S., Delta sets for divisors supported in two points, Finite Fields Appl., vol. 18, no. 5, pp. 865-885, 2012.
Duursma, I., Mak, K., On maximal curves which are not Galois subcovers of the Hermitian curve, Bull. Braz. Math. Soc. (N.S.), vol. 43, no. 3, pp. 453-465, 2012.


Couvreur, A., Duursma, I., Evaluation codes from smooth quadric surfaces and twisted Segre varieties, Des. Codes Cryptogr., vol. 66, no. 1-3, pp. 291-303, 2013.
Duursma, I., Mak, K., On lower bounds for the Ihara constants A(2) and A(3), to appear in Compos. Math. Preprint available on arXiv.

   Proceedings

Duursma, I., On the decoding procedure of Feng and Rao, Proceedings Algebraic and Combinatorial Coding Theory III, Voneshta Voda, Bulgaria, pp. 64-67, June, 1992.
Duursma, I., Partition designs on divisor class groups and weight distributions, Proceedings Joint Russian-Swedish Workshop on Information Theory VI, M{\"o}lle, Sweden, pp. 128-131, August, 1993.
Duursma, I. and Koetter, R., Error-locating pairs for cyclic codes, Proceedings Joint Russian-Swedish Workshop on Information Theory VI, M{\"o}lle, Sweden, pp. 123-127, August, 1993.
Duursma, I., On erasure decoding of AG-codes, Proceedings IEEE Information Theory Workshop, Moscow, Russia, July, 1994.
Duursma, I., Average weight distributions for AG-codes, Proceedings Algebraic and Combinatorial Coding Theory IV, Novgorod, Russia, September, 1994.


Duursma, I., On termination criteria for decoding algorithms, Proceedings EIDMA Winter Meeting, Veldhoven, The Netherlands, p. 50, December, 1994.
Bonnecaze, A. and Duursma, I., The association scheme for the Preparata codes, Thirty-Third Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois, USA, pp. 908-910, October, 1995.
Duursma, I., Class numbers for some hyperelliptic curves, in: Arithmetic, geometry and coding theory (Luminy, 1993), pp. 45-52, de Gruyter, Berlin, 1996.
Duursma, I., Stichtenoth, H., and Voss, C., Generalized Hamming weights for duals of BCH codes, and maximal algebraic function fields, in: Arithmetic, geometry and coding theory (Luminy, 1993), pp. 53-65, de Gruyter, Berlin, 1996.
Duursma, I., BCH codes over fields and over rings, in: Arithmetic geometry and Algorithms in the theory of error correcting codes Pointe-{\`a}-Pitre, Guadeloupe, 4 pages, April, 1996.


Duursma, I. and Boutros, J., Lattices and codes over rings, Thirty-Fourth Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois, USA, pp. 322-324, October, 1996.
Duursma, I., Quadratic residue codes and hyperelliptic curves, Thirty-Fifth Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois, USA, pp. 41-43, October, 1997.
Duursma, I., Interpolation and approximation in decoding, Proceedings IEEE Information Theory Workshop, Killarney, Ireland, p. 37, June, 1998.
Duursma, I., From weight enumerators to zeta functions, Thirty-Seventh Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois, USA, September, 1999.
Duursma, I. and Sakurai, K., Efficient algorithms for the Jacobian variety of hyperelliptic curves $y^2=x^p-x+1$ over a finite field of odd characteristic $p$, in: Coding theory, cryptography and related areas (Guanajuato, 1998), pp. 73-89, Springer, Berlin, 2000.


Duursma, I., Gaudry, P., and Morain, F., Speeding up the discrete log computation on curves with automorphisms, in: Advances in Cryptology - ASIACRYPT'99 (Singapore), pp. 103-121, Lecture Notes in Computer Science, vol. 1716, Springer, Berlin, 1999.
Duursma, I., A Riemann hypothesis analogue for self-dual codes, in: Codes and Association schemes (Piscataway, NJ, 1999), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 56, pp. 115-124, AMS, Providence, RI, 2001.
Duursma, I. and Enjalbert, J.-Y.,Bounds for completely decomposable Jacobians, in: Finite fields with applications to coding theory, cryptography and related areas (Oaxaca, 2001), pp. 86-93, Springer, Berlin, 2002.
Duursma, I., Results on zeta functions for codes, in: Proceedings of Fifth Conference on Algebraic Geometry, Number Theory, Coding Theory and Cryptography, University of Tokyo, January 17-19, 2003.
Duursma, I. and Lee, H.-S., Tate pairing implementations for hyperelliptic curves $y^2=x^p-x+d$, in: Advances in Cryptology - ASIACRYPT 2003, pp. 111-123, Lecture Notes in Computer Science, vol. 2894, Springer, Berlin, 2003.


Duursma, I., Combinatorics of the two-variable zeta function, in: Finite Fields and Applications, %7th International Conference, Fq7, May 2003, Eds. Mullen, Poli, Stichtenoth, Springer LNCS 2948. pp. 109-136, Lecture Notes in Computer Science, vol. 2948, Springer, Berlin, 2004.
Duursma, I., Poonen, B., and Zieve, M., Everywhere ramified towers of global function fields, in: Finite Fields and Applications, %7th International Conference, Fq7, May 2003, Eds. Mullen, Poli, Stichtenoth, Springer LNCS 2948. pp. 148-153, Lecture Notes in Computer Science, vol. 2948, Springer, Berlin, 2004.
Duursma, I. and Kirov, R., An extension of the order bound for AG codes, in: Proceedings AAECC-18 (Applied algebra, Algebraic algorithms and Error Correcting Codes), pp. 11-22, Lecture Notes in Computer Science, vol. 5527, Springer, Berlin, 2009.

   Other

Duursma, I., Twisted Klein curves modulo 2, ArXiv preprint Math.NT/0302154.
Duursma, I. and Greferath, M., Computing Symmetrized weight enumerators for lifted quadratic residue codes, ArXiv preprint Math.CO/0302132.