Jacobiennes et Cryptographie (Universit'e de Limoges).
Bounds for completely decomposable Jacobians. Finite fields with applications to coding theory, cryptography and related areas (Oaxaca, 2001), 86--93, Springer, Berlin, 2002. Full paper, Review (for the last line in the review read m>=4 instead of m>4)
Fall 2003 - : Universit'e Lille 2, France.

April 2007, Jennifer Paulhus Homepage

Elliptic factors in Jacobians of low genus curves.
Decomposing Jacobians of curves with extra automorphisms. Acta Arith. 132 (2008), no. 3, 231--244. Full paper, Review
Fall 2007 - : Department of Mathematics, Kansas State University, Manhattan, KS / Department of Mathematical Sciences Villanova University, Villanova, PA / now at Department of Mathematics and Statistics, Grinnell College, Iowa.

May 2007, Samuel Kadziela

Rigid analytic uniformization of hyperelliptic curves.
Rigid analytic uniformization of curves and the study of isogenies. Acta Appl. Math. 99 (2007), no. 2, 185--204. Full paper, Review
Fall 2007 - : Department of Mathematics, University of California, Irvine, CA / now at CTC Chicago Trading Company

August 2007, Seung Kook Park (Old) Homepage

Applications of algebraic curves to cryptography.
Minimum distance of Hermitian two-point codes. To appear in Designs, Codes, and Cryptography. [arXiv]
Fall 2007 - : Department of Mathematical Sciences, University of Cincinnati, OH / KIAS, Korea / now at Sookmyung Women's University, Korea.

June 2010, Radoslav Kirov Homepage

Bounds on parameters of algebraic geometric codes and secret sharing schemes.
An extension of the order bound for AG codes, Iwan M. Duursma and Radoslav Kirov. In: Proceedings AAECC-18, Springer LNCS 5527, pages 11-22, 2009. [arXiv]
Distance bounds for algebraic geometric codes, Iwan Duursma, Radoslav Kirov and Seungkook Park, January 2010, submitted. [arXiv]
Fall 2010 - : Nanyang Technological University, Singapore / soon at Google, California.

2007, Qingquan Wu (As Co-Advisor; Advisor: Renate Scheidler, U Calgary)

2009, Eric Landquist (As Co-Advisor; Advisor: Renate Scheidler, U Calgary)

Advising towards degree:

Abdulla Eid
Kit Ho Mak

Other publications by students

The Vector Decomposition Problem for Elliptic and Hyperelliptic Curves, Iwan Duursma and Negar Kiyavash, J. Ramanujan Math. Soc. 20 (2005), no. 1, 59--76. [.pdf] [.ps] (scanned version in pdf of the paper [Yos03] by Yoshida)

Abstract: The group of m-torsion points on an elliptic curve, for a prime number m, forms a two-dimensional vector space. It was suggested and proven by Yoshida that under certain conditions the vector decomposition problem (VDP) on a two-dimensional vector space is at least as hard as the computational Diffie-Hellman problem (CDHP) on a one-dimensional subspace. In this work we show that even though this assessment is true, it applies to the VDP for m-torsion points on an elliptic curve only if the curve is supersingular. But in that case the CDHP on the one-dimensional subspace has a known sub-exponential solution. Furthermore, we present a family of hyperelliptic curves of genus two that are suitable for the VDP.

A generalized floor bound for the minimum distance of geometric Goppa codes, Benjamin Lundell and Jason McCullough, J. Pure Appl. Algebra 207 (2006), no. 1, 155--164.

Abstract: We prove a new bound for the minimum distance of geometric Goppa codes that generalizes two previous improved bounds. We include examples of the bound applied to one- and two-point codes over certain Suzuki and Hermitian curves.

Geometric Reed-Solomon codes of length 64 and 65 over F8, Chien-Yu Chen and Iwan Duursma, IEEE Trans. on Inform. Theory, vol. 49, pp. 1351-1353, May 2003. [.ps]

Abstract: We determine the actual parameters for a class of one-point codes of length 64 and 65 over F_8 defined by Hansen-Stichtenoth. Several codes have a minimum distance that exceeds the Feng-Rao bound. The codes with parameters [64,5,51], [64,10,43],[64,11,42], [64,12,40], [65,5,52],[65,10,43],[65,11,42],[65,12,41],[64,13,40] are better than any known code.