GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 47 (2013) no. 4, pp. 371-388.

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.

DOI: 10.1051/ita/2013043
Classification: 11T71,  14G50,  94A60
Keywords: arithmetic cross-correlation, Legendre symbol, primitive sequence, cyclically distinct
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     title = {GLS: {New} class of generalized {Legendre} sequences with optimal arithmetic cross-correlation},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
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WANG, Huijuan; WEN, Qiaoyan; ZHANG, Jie. GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 47 (2013) no. 4, pp. 371-388. doi : 10.1051/ita/2013043. http://www.numdam.org/articles/10.1051/ita/2013043/

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