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

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

2007-02-23

arxiv.org/abs/cs/0702139v1

Computer Science

Cryptography and Security

23 pages

Scientific paper

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.

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