Research Interests

• curves over finite fields
• Goppa codes
• genus calculations
• lattice constructions and theta functions
• quantum codes
• asymptotically good towers of curves

Papers

• (with T. Shaska) "Quantum codes from algebraic geometry codes and their automorphism groups", (work in progress).


• (with T. Shaska, S. Wijesiri) "Codes, modular lattices, and corresponding theta functions", (submitted).


• "Genus calculations for towers of function fields arising from equations of $C_{a,b}$ curves", (work in progress).


• "On the construction of codes from an asymptotically good tower over $F_8$", Serdica J. Computing 1 (2007), no. 2, 171--184. Download.


• (with T. Shaska) "Non-bilinear codes over $F_{p^2}$ and $F_p \times F_p$, Hermitian lattices, and corresponding theta functions," Advances in Coding Theory and Cryptography, vol 3, 2007, pg 70-80. Download.

Selected Talks

• "Codes over $F_{p^2}$ and $F_p \times F_p$, lattices, and theta functions," Applications of Computer Algebra, Oakland University, July 2007. (Coding Theory and Cryptography session co-organizer)


• "An Introduction to Elliptic Curves," Bates College, May, 2007.


• "Error-Correcting Codes - Theory and Applications," Boston University MAA Masterclass, April, 2007.


• "Genus calculations for towers of function fields arising from equations of $C_{ab}$ curves," Session on Computational Algebraic and Analytic Geometry for Low-Dimensional Varieties, Joint Mathematics Meetings, New Orleans, LA, January, 2007.


• "Genus calculations - counting gaps with postage stamps," Bates College Math Department Seminar, November, 2006.


• "On the geometric construction of codes from an asymptotically good tower over GF(8)," 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.


• "Genus calculations for towers of function fields arising from equations of $C_{ab}$ curves," Conference on Computational Aspects of Algebraic Curves, University of Idaho, May, 2005.