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On the linear complexity of feedback registers

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3 Author(s)
Chan, A.H. ; Coll. of Comput. Sci., Northeastern Univ., Boston, MA, USA ; Goresky, M. ; Klapper, A.

Sequences generated by arbitrary feedback registers (not necessarily feedback shift registers) with arbitrary feedforward functions are studied. The definition of linear complexity of a sequence is generalized to the notions of strong and weak linear complexity of feedback registers. A technique for finding upper bounds for the strong linear complexities of such registers is developed. This technique is applied to several classes of registers. It is shown that a feedback shift register in which the feedback function is of the form x 1+h(x2, . . . , xn ) can generate long periodic sequences with high linear complexities only if its linear and quadratic terms have certain specific forms

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Information Theory, IEEE Transactions on  (Volume:36 ,  Issue: 3 )