Algebraic Geometric Codes

Description:

"Whereas most books on coding theory build up coding theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, this book constantly looks for interpretations that connect coding theory to algebraic geometry and number theory. There are no prerequisites other than a standard algebra graduate course. The first two chapters of the book can serve as an introduction to coding theory and algebraic geometry respectively. Special attention is given to the geometry of curves over finite fields in the third chapter. Finally, in the last chapter the authors explain relations between all of these: the theory of algebraic geometric codes."--Jacket.

subjects: Algebraic Geometry,  Coding theory,  Number theory,  Mathematical theory of computation,  Mathematics,  Computers - General Information,  Science/Mathematics,  Information Theory,  Nonfiction,  Advanced,  Geometry, Algebraic,  Curves,  Information and communication, circuits,  Theory of error-correcting codes and error-detecting codes,  Arithmetic problems. Diophantine geometry,  Finite ground fields,  Algebraic number theory: global fields,  Arithmetic theory of algebraic function fields,  Algebraic numbers; rings of algebraic integers,  Finite fields and commutative rings (number-theoretic aspects),  Algebraic coding theory; cryptography,  Zeta and $L$-functions: analytic theory,  Zeta and $L$-functions in characteristic $p$,  Class field theory,  Zeta functions and $L$-functions of number fields,  Families, fibrations,  Fine and coarse moduli spaces,  Surfaces and higher-dimensional varieties,  Arithmetic ground fields,  Algebraische meetkunde,  Coderingstheorie,  Codage,  Theorie des Nombres,  Geometrie algebrique