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Differential approach for the study of duals of algebraic-geometric codes on surfaces

Alain Couvreur (2011)

Journal de Théorie des Nombres de Bordeaux

The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this description is less trivial, it can be regarded as a natural extension to surfaces of the result asserting that the dual of a functional code C L ( D , G ) on a curve is the differential code C Ω ( D , G ) . We study the parameters of such codes and state a lower bound for their minimum distance. Using this bound, one can study some examples...

Equivalences between elliptic curves and real quadratic congruence function fields

Andreas Stein (1997)

Journal de théorie des nombres de Bordeaux

In 1994, the well-known Diffie-Hellman key exchange protocol was for the first time implemented in a non-group based setting. Here, the underlying key space was the set of reduced principal ideals of a real quadratic number field. This set does not possess a group structure, but instead exhibits a so-called infrastructure. More recently, the scheme was extended to real quadratic congruence function fields, whose set of reduced principal ideals has a similar infrastructure. As always, the security...

Currently displaying 101 – 120 of 497