The weights of the orthogonals of the extended quadratic binary Goppa codes

Starting from results on elliptic curves and Kloosterman sums over the finite field GE(2^t), the authors determine the weights of the orthogonals of some binary linear codes; the Melas code of length, the irreducible cyclic binary code of length 2^t+1, and the extended binary Goppa codes defined by polynomials of degree two