Overview: Serves as an introduction and invitation to several main directions of research in the area of Function Fields over Finite Fields and their various applications to Information Theory.Reasonably access.The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory, such as coding theory, sphere packings and lattices, sequence design, and cryptography. The use of function fields o
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