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 generalization of linear recurring relations. The concept of minimal polynomial set of such relations is established. Some of their important properties are presented, such as the agreement theorem. And on this basis, an algorithm for computing a minimal polynomial set of such relations is developed, which is a generalization of the Berlekamp\|Massey algorithm, and its complexity is discussed.