On Shortest Linear Recurrence Of Multi-sequences

The fundamental iterative algorithm(FIA) is used to synthesize whnimum lengthlinear feedback shift registers fOr generating prescribed multiple sequences over field.Inrecent years how to generalize it to an arbitrary integral domain has become a problemof great concern. This paper first presents the iterative algorithm for solving the problemof the shortest linear recurrences of two sequences .The theorems guarantee that thepolynomial obtained is the drinimal polynomial. Further more the algorithm for recurringminimal polynomial of multi-sequences is presented .So the problem about shortest linearrecurrence of multiple sequences over an integral domain is solved.