m-Sequences of Lengths 22k 1 and 2k - 1 with at Most Four-Valued Cross Correlation

Authors:
Tor Helleseth;Alexander Kholosha
Affiliations:
The Selmer Center Department of Informatics, University of Bergen, Bergen, Norway N-5020;The Selmer Center Department of Informatics, University of Bergen, Bergen, Norway N-5020
Venue:
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Year:
2008

Citing 6
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Abstract

Considered is the distribution of the cross correlation betweenm-sequences of length 2 m- 1, wheremis even, and m-sequences of a shorter length 2m/2- 1. Pairs of this type with at mostfour-valued cross correlation are found and the completecorrelation distribution is determined. These results cover thetwo-valued Kasami case and all three-valued decimations foundearlier. Conjectured is that there are no other cases leading to atmost four-valued cross correlation apart from the ones proven hereand except for a single, seemingly degenerate, case.