Algebraic Function Fields and Codes

Rating:
Summary: an introduction to Goppa codes
Review: Coding theory is fundamental to make digital transmission technology work efficiently and usually uses Reed-Solomon codes. The "natural" extension of those codes is to consider riemann surfaces over finite fields.

The theory is developped from scratch and does not assume any knowledge of algebraic geometry. The author gave a proof of the Hasse-Weil bounds using the Zeta function. In parallel the theory of linear codes and Goppa codes is introduced from the beginning.

While the author do not consider the geometry of riemann surfaces, having a knowledge of riemann surfaces over C can help a lot.
This short book should be considered as a very nice introduction to geometric goppa codes.

Rating:
Summary: an introduction to Goppa codes
Review: Coding theory is fundamental to make digital transmission technology work efficiently and usually uses Reed-Solomon codes. The "natural" extension of those codes is to consider riemann surfaces over finite fields.

The theory is developped from scratch and does not assume any knowledge of algebraic geometry. The author gave a proof of the Hasse-Weil bounds using the Zeta function. In parallel the theory of linear codes and Goppa codes is introduced from the beginning.

While the author do not consider the geometry of riemann surfaces, having a knowledge of riemann surfaces over C can help a lot.
This short book should be considered as a very nice introduction to geometric goppa codes.