Decoding algebraic-geometric codes over elliptic curves when the number of errors exceeds half of the designed distance

V. M. Sidelnikov [3] constructed decoding algorithms for Reed-Salomon codes when the number of errors exceeds half of the true minimum distance. We consider analogous methods for decoding algebraic-geometric codes over elliptic curves. If the number of errors t exceeds (d* - 1)/2, where d* is the designed distance, the decoding problem is reduced to the problem of finding the common zeros of two polynomials, whose coefficients depend upon the known syndroms: O(t+1)((0)) (Z(1),...,Z(r)), O(t+1)((1)) (Z(1),...,Z(r)) (we assume that variables Z(i) take the values on a given affine elliptic curve X, and that r = 2t - d* + 2).