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.

Classification: 11T71, 14G50, 94A60

Keywords: arithmetic cross-correlation, Legendre symbol, primitive sequence, cyclically distinct

@article{ITA_2013__47_4_371_0, author = {WANG, Huijuan and WEN, Qiaoyan and ZHANG, Jie}, title = {GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, publisher = {EDP-Sciences}, volume = {47}, number = {4}, year = {2013}, pages = {371-388}, doi = {10.1051/ita/2013043}, mrnumber = {3132297}, language = {en}, url = {http://www.numdam.org/item/ITA_2013__47_4_371_0} }

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/item/ITA_2013__47_4_371_0/

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