On the distribution of de Bruijn sequences of given complexity
Tuvi Etzion, Abraham Lempel · IEEE Transactions on Information Theory · 1984
The distribution\gamma (c, n)of de Bruijn sequences of ordernand linear complexitycis investigated. It is shown that forn \geq 4, \gamma (2^{n} - 1, n) \equiv 0 \pmod{8}, and fork \geq 3, \gamma (2^{2k} - 1,2k) \equiv 0 \pmod{l6}. It is also shown that\gamma (c, n) \equiv 0 \pmod{4}for allc, andn \geq 3such thatcnis even.