Codes on Algebraic Curves

"Codes on Algebraic Curves" is a comprehensive introduction to the theory of algebraic curves over finite fields and geometric Goppa codes. The book is divided into four main parts. The first part provides a brief overview of the fundamental concepts and facts of error-correcting code theory. The second part is dedicated to an in-depth exploration of the theory of algebraic curves, particularly those defined over finite fields. The third part details the theory of classical modular curves and their reduction modulo a prime number. The fourth part addresses the construction of geometric Goppa codes and the generation of asymptotically good linear codes derived from algebraic curves over finite fields. These topics connect the abstract theory of algebraic curves with practical challenges in information transmission.