Proof of a Conjecture of Helleseth: Maximal Linear Recursive Sequences of Period $2^{2^n}-1$ Never Have Three-Valued Cross-Correlation

preprint2011arXivOpen access

We prove a conjecture of Helleseth that claims that for any $n \geq 0$ , a pair of binary maximal linear sequences of period $2^{2^n}-1$ can not have a three-valued cross-correlation function.

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Proof of a Conjecture of Helleseth: Maximal Linear Recursive Sequences of Period $2^{2^n}-1$ Never Have Three-Valued Cross-Correlation

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Proof of a Conjecture of Helleseth: Maximal Linear Recursive Sequences of Period 22n−12^{2^n}-122n−1 Never Have Three-Valued Cross-Correlation

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Proof of a Conjecture of Helleseth: Maximal Linear Recursive Sequences of Period $2^{2^n}-1$ Never Have Three-Valued Cross-Correlation