Abstract
Given an m-sequence, the main factor influencing the least period of the Generalized Self-Shrinking (GSS) sequence is the selection of the linear combining vector G. Based on the calculation of the minimal polynomial of L GSS sequences and the comparison of their degrees, an algorithm for selecting the linear combining vector G is presented, which is simple to understand, to implement and to prove. By using this method, much more than 2L−1 linear combining vectors G of the desired properties will be resulted. Thus in the practical application the linear combining vector G can be chosen with great arbitrariness. Additionally, this algorithm can be extended to any finite field easily.
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