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

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Rueppel has conjectured that, for allngeq 1, the subsequence consisting of the firstndigits of the binary sequence(1,1,0,1,0,0,0,1,0^{7},1,0^{15},1, cdots )has linear complexitylfloor (n + 1)/2 rightfloor. This conjecture is proved, and a minimum length generator is found for eachn. The proof utilizes properties of an element in an extension field of the field of rational functions over GF(2).

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