Decoding of Codes on an Elliptic Curve with Number of Errors Greater than Half the Designed Code Distance

The problem of decoding algebraic-geometric codes over an elliptic curve is considered, where the number of errors may exceed half the designed code distance (in particular, it may exceed half the minimum distance as well). This problem can be reduced to that of finding zeroes of a multivariate polynomial. A syndrome probabilistic decoding algorithm of depth $t$ is constructed.