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On the distribution of de Bruijn sequences of given complexity

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2 Author(s)

The distribution \gamma (c, n) of de Bruijn sequences of order n and linear complexity c is investigated. It is shown that for n \geq 4, \gamma (2^{n} - 1, n) \equiv 0 \pmod {8} , and for k \geq 3, \gamma (2^{2k} - 1,2k) \equiv 0 \pmod {l6} . It is also shown that \gamma (c, n) \equiv 0 \pmod {4} for all c , and n \geq 3 such that cn is even.

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Information Theory, IEEE Transactions on  (Volume:30 ,  Issue: 4 )