Linear complexity of de Bruijn sequences-old and new results

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 2/sup n/ is bounded below by 2/sup n-1/+n and above by 2/sup n-/1 for n/spl ges/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/sup [log n]+1/ in the above range, there exist binary de Bruijn sequences of length 2/sup n/ with linear complexity in the interval.