Abstract
If s = ( s 0, s 1,…, s 2 n −1 ) is a binary de Bruijn sequence of span n, then it has been shown that the least length of a linear recursion that generates s, called the complexity of s and denoted by c(s), is bounded for n ⩾ 3 by 2 n − 1 + n ⩽ c(s) ⩽ 2 n −1. A numerical study of the allowable values of c(s) for 3 ⩽ n ⩽ 6 found that all values in this range occurred except for 2 n−1 + n + 1. It is proven in this note that there are no de Bruijn sequences of complexity 2 n−1 + n + 1 for all n ⩾ 3.
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