GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation

The Legendre symbol has been used to construct sequences with ideal cross-correlation, but it was never used in the arithmetic cross-correlation. In this paper, a new class of generalized Legendre sequences are described and analyzed with respect to their period, distributional, arithmetic cross-correlation and distinctness properties. This analysis gives a new approach to study the connection between the Legendre symbol and the arithmetic cross-correlation. In the end of this paper, possible application of these sequences with optimal arithmetic cross-correlation is indicated.

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[17]  This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. 1 Arithmetic Correlations and Walsh Transforms , 2022 .