Calderbank, AR; McGuire, G; Poonen, B; Rubinstein, M, *On a conjecture of Helleseth regarding pairs of binary m-sequences*,
Ieee Transactions on Information Theory, vol. 42 no. 3
(1996),
pp. 988-990 [doi] .
**Abstract:**

*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 /«-sequences, the crosscorrelation function must take on at least three values. This correspondence addresses a conjecture made by Helleseth in 1976, that if rn 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. © 1996 IEEE.*