In this tract, Professor Moreno develops the theory of algebraic
curves over finite fields, their zeta and L-functions, and, for the
first time, the theory of algebraic geometric Goppa codes on
algebraic curves. Among the applications considered are: the
problem of counting the number of solutions of equations over
finite fields; Bombieri's proof of the Reimann hypothesis for
function fields, with consequences for the estimation of
exponential sums in one variable; Goppa's theory of
error-correcting codes constructed from linear systems on algebraic
curves; there is also a new proof of the TsfasmanSHVladutSHZink
theorem. The prerequisites needed to follow this book are few, and
it can be used for graduate courses for mathematics students.
Electrical engineers who need to understand the modern developments
in the theory of error-correcting codes will also benefit from
studying this work.
Cambridge University Press (Virtual Publishing)
|Country of origin:
||Cambridge Tracts in Mathematics, 97
||Electronic book text
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