Euclidean modules and multisequence synthesis

Abstract

In this paper we extend the concept of Euclidean ring in commutative rings to arbitrary modules and give a special Euclidean Fq[x]-module Kn, where Fq is a finite field, n a positive integer and K = Fq((x-1)). Thus a generalized Euclidean algorithm in it is deduced by means of Fq[x]-lattice basis reduction algorithm. As its direct application, we present a new multisequence synthesis algorithm completely equivalent to Feng-Tzeng’ generalized Euclidean synthesis algorithm. In addition it is also equivalent to Mills continued fractions algorithm in the case of the single sequence synthesis.