Abstract
In this paper we extend the concept of Euclidean ring in commutative rings to arbitrary modules and give a special Euclidean F q[x]-module K n, where F q is a finite field, n a positive integer and K = F q((x-1)). Thus a generalized Euclidean algorithm in it is deduced by means of F q[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.
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