I this talk given at the 3rd European Congress of Mathematics (3ECM, Barcelona, Spain, July 2000), we illustrate how the computer algebra system MAGMA can be used for the implementation of sophisticated algorithms requiring many primitives in various branches of effective mathematics like finite fields, algebraic geometry or error-correcting codes. We give the example of the construction of Goppa’s algebraic-geometric codes in this system.

This is a joint work with Pawel WOCJAN.