Codes and Elliptic Curves
In this paper we discuss recent results (, , , , , ) on codes and algebraic curves. We are not concerned with algebraic geometric Goppa codes but rather with another link between coding theory and algebraic geometry. In our case the codes correspond to families of algebraic curves over a finite field, whereas Goppa codes come from a fixed algebraic curve. We use algebraic geometry to determine the weight distributions of certain codes but also we show that results from coding theory may be used to obtain results about the variation of the number of points in families of algebraic curves over a finite field. We do not assume that the reader has a knowledge of coding theory.
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