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Linear complexity of de Bruijn sequences-old and new results

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1 Author(s)
Etzion, T. ; Dept. of Comput. Sci., Technion-Israel Inst. of Technol., Haifa

The linear complexity of a de Bruijn sequence is the degree of the shortest linear recursion which generates the sequence. It is well known that the complexity of a binary de Bruijn sequence of length 2n is bounded below by 2n-1+n and above by 2n-1 for n⩾3. We briefly survey the known knowledge in this area. Some new results are also presented, in particular, it is shown that for each interval of length 2[log n]+1 in the above range, there exist binary de Bruijn sequences of length 2n with linear complexity in the interval

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Information Theory, IEEE Transactions on  (Volume:45 ,  Issue: 2 )