Abstract
Considered is the distribution of the cross correlation between m-sequences of length 2m − 1, where m is even, and m-sequences of a shorter length 2m/2− 1. Pairs of this type with at most four-valued cross correlation are found and the complete correlation distribution is determined. These results cover the two-valued Kasami case and all three-valued decimations found earlier. Conjectured is that there are no other cases leading to at most four-valued cross correlation apart from the ones proven here and except for a single, seemingly degenerate, case.
This work was supported by the Norwegian Research Council.
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References
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Helleseth, T., Kholosha, A. (2008). m-Sequences of Lengths 22k− 1 and 2k − 1 with at Most Four-Valued Cross Correlation. In: Golomb, S.W., Parker, M.G., Pott, A., Winterhof, A. (eds) Sequences and Their Applications - SETA 2008. SETA 2008. Lecture Notes in Computer Science, vol 5203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85912-3_10
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DOI: https://doi.org/10.1007/978-3-540-85912-3_10
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