Characterization of $m$-Sequences of Lengths $2^{2k}-1$ and $2^k-1$ with Three-Valued Crosscorrelation

Abstract

Considered is the distribution of the crosscorrelation between $m$-sequences of length $2^m-1$, where $m=2k$, and $m$-sequences of shorter length $2^k-1$. New pairs of $m$-sequences with three-valued crosscorrelation are found and the complete correlation distribution is determined. Finally, we conjecture that there are no more cases with a three-valued crosscorrelation apart from the ones proven here.