Abstract
ABSTRACT Let for some and consider the extension with . We consider families of curves of the form . We call such families Artin-Schreier families, even though not every curve in need be an Artin-Schreier curve. It is easy to see that the members of such a family can have at most affine -rational points. Using a well-known coding theory technique, we determine the condition under which can attain this bound and we obtain some simple, but interesting, corollaries of this result. One of these consequences shows the existence of maximal curves of Artin-Schreier type. Our main result is important for minimum distance analysis of certain two-dimensional cyclic codes.
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