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Proof of Rueppel's linear complexity conjecture (Corresp.)

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Rueppel has conjectured that, for all n\geq 1 , the subsequence consisting of the first n digits of the binary sequence (1,1,0,1,0,0,0,1,0^{7},1,0^{15},1, \cdots ) has linear complexity \lfloor (n + 1)/2 \rfloor . This conjecture is proved, and a minimum length generator is found for each n . The proof utilizes properties of an element in an extension field of the field of rational functions over GF (2) .

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IEEE Transactions on Information Theory  (Volume:32 ,  Issue: 3 )