no. 4
GLS: New class of generalized Legendre sequences with optimal arithmetic cross-correlation
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 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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     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},
     pages = {371--388},
     year = {2013},
     publisher = {EDP Sciences},
     volume = {47},
     number = {4},
     doi = {10.1051/ita/2013043},
     mrnumber = {3132297},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ita/2013043/}
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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, Tome 47 (2013) no. 4, pp. 371-388. doi: 10.1051/ita/2013043

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