A type of recurring relation on sequences and efficient decoding of a class of algebraic-geometric codes (I) - A new type of recurring relation

A new type of recurring relation is introduced on sequences, which is a gen eralization of linear recurring relations. The concept of minimal polynomia l set of such relations is established. Some of their important properties are presented, such as the agreement theorem. And on this basis, an algorit hm for computing a minimal polynomial set of such relations is developed, w hich is a generalization of the Berlekamp-Massey algorithm, and its complex ity is discussed.