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Weights in Codes and Genus 2 Curves
Gary McGuire, Jose Felipe Voloch
We discuss a class of binary cyclic codes and their dual codes. The minimum distance is determined using algebraic geometry, and an application of Weil's theorem. We relate the wei…
Diophantine approximation and deformation
Minhyong Kim, Dinesh S. Thakur, José Felipe Voloch
We associate certain curves over function fields to given algebraic power series and show that bounds on the rank of Kodaira-Spencer map of this curves imply bounds on the exponent…
Difference subgroups of commutative algebraic groups over finite fields
Thomas Scanlon, José Felipe Voloch
The work of Chatzidakis and Hrushovski on the model theory of difference fields in characteristic zero showed that groups defined by difference equations have a very restricted str…
Torsion points on y^2=x^6+1
José Felipe Voloch
Let C be the curve y^2=x^6+1 of genus 2 over a field of characteristic zero. Consider C embedded in its Jacobian J by sending one of the points at infinity on C to the origin of J.…