On a fast decoding of multipoint codes from algebraic curves

Abstract

Multipoint codes are a broad class of algebraic geometry codes derived from algebraic functions which have multiple poles on their defining curves. Thus, they are more general than one-point codes which are an important class of algebraic codes in the sense that they can be decoded efficiently by using the BMS algorithm. In this paper we present a fast decoding method of multipoint codes from algebraic curves. Since algebraic geometry codes from algebraic curves are essentially the same as multipoint codes, this means that almost all algebraic geometry codes can be decoded efficiently.