A type of recurring relations on sequences and efficient decoding of a class of algebraic-geometric codes

A type of recurring relation is introduced on sequences. Some properties of this type of recurring relations are established and an algorithm for computing a minimal polynomial set of this type of recurring relation is presented. Then an efficient decoding algorithm up to half the Feng-Rao bound for a class of algebraic-geometric codes is proposed by developing a majority voting scheme of the recurring relation on the syndrome sequence of an error vector.