Majority coset decoding

A majority coset decoding (MCD) procedure that can be applied to an arbitrary geometric code is discussed. In general, the basic algorithm for decoding of algebraic-geometric codes does not correct up to the designed minimum distance. In MCD, a reduction step is added to the basic algorithm. In case the basic algorithm fails, a majority scheme is used to obtain an additional syndrome for the error vector. Thus a strictly smaller cost containing the error vector is obtained. In this way, the basic algorithm is applied to a decreasing chain of cosets and after finitely many steps the coset will be small enough for successful application of the basic algorithm.