Spectra of Algebraic-Geometric Codes

We derive bounds on the enumerator of an arbitrary algebraic-geometric code. We calculate in full the weight distribution of the code constructed from all the points of an elliptical curve. The weight distribution (the enumerator) is found to depend on the group of points of this curve and on an element of this group. The number of minimum-weight vectors is minimized both by elements and by curves. The possibility that such a code is an MDS code is explored.