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On a conjecture of Helleseth regarding pairs of binary m-sequences

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4 Author(s)
A. R. Calderbank ; AT&T Bell Labs., Murray Hill, NJ, USA ; G. McGuire ; B. Poonen ; M. Rubinstein

Binary m-sequences are maximal-length sequences generated by shift registers of length m, that are employed in navigation, radar, and spread-spectrum communication. It is well known that given a pair of distinct m-sequences, the crosscorrelation function must take on at least three values. This correspondence addresses a conjecture made by Helleseth in 1976, that if m is a power of 2, then there are no pairs of binary m-sequences with a 3-valued crosscorrelation function. This conjecture is proved under the assumption that the three correlation values are symmetric about -1

Published in:

IEEE Transactions on Information Theory  (Volume:42 ,  Issue: 3 )