08.01.2009

We discuss the problem of determining the weight distribution of linear codes on elliptic curves. It is shown that the weight enumerators of non-MDS elliptic codes are completely determined by the number of minimum weight codewords. Using the structure of the group of rational points of the curves in question, we give a procedure to determine the number of minimum weight codewords. For two classes of elliptic codes we shall give explicit formulas for this number. Several examples are presented.