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arXiv · 2212.10953

Quaternary Legendre Pairs

Ilias S. Kotsireas·Arne Winterhof
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Abstract

We introduce quaternary Legendre pairs of length $\ell$. In contrast to binary Legendre pairs they can exist for even $\ell$ as well. First we show that they are pertinent to the construction of quaternary Hadamard matrices of order $2\ell+2$ and thus of binary Hadamard matrices of order $4\ell+4$. Then for a prime $p>2$ we present a construction of a pair of sequences of length $p$ from which we can derive quaternary Legendre pairs of length $\ell=2p$ by decompression for $p=3,5,7,13,19,31,41$. Moreover, we give also constructions of Legendre pairs of length $\ell$ for all remaining even $\ell\le 24$.

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Ilias S. Kotsireas, Arne Winterhof. 2022-12-21. Quaternary Legendre Pairs. https://arxiv.org/abs/2212.10953

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