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On the quadratic spans of DeBruijn sequences

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2 Author(s)
Chan, A.H. ; Mitre Corp., Bedford, MA, USA ; Games, R.

The quadratic span of a periodic binary sequence is defined to be the length of the shortest quadratic feedback shift register (FSR) that generates it. An algorithm for computing the quadratic span of a binary sequence is described. The required increase in quadratic span is determined for the special case of when a discrepancy occurs in a linear FSR that generates an initial portion of a sequence. The quadratic spans of binary DeBruijn sequences are investigated. An upper bound for the quadratic span of a DeBruijn sequence of span n is given; this bound is attained by the class of DeBruijn sequences obtained from m -sequences. It is easy to see that a lower bound is n+1, but a lower bound of n+2 is conjectured. The distributions of quadratic spans of DeBruijn sequences of span 3, 4, 5 and 6 are presented

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Information Theory, IEEE Transactions on  (Volume:36 ,  Issue: 4 )