Register synthesis for algebraic feedback shift registers based on non-primes (Q1878294)

This paper deals with a synthesis problem for an extended class of algebraic feedback shift registers defined by \textit{A. Klapper} and \textit{J. Xu} [Theor. Comput. Sci. 226, No. 1--2, 61--92 (1999; Zbl 0965.94014); see also Proc. SETA `98, Discrete Mathematics and Theoretical Computer Science, 379--392 (1999; Zbl 1015.94540) and \textit{A. Klapper} and \textit{M. Goresky}, Lect. Notes Comput. Sci. 809, 174--178 (1994; Zbl 0943.94515), J. Cryptology 10, 111--147 (1997; Zbl 0874.94029)]. Several cases where the register synthesis problem can be solved by an efficient algorithm - the adequate modification of the Berlekamp-Massey algorithm - are discussed.