Abstract
Pseudo-random sequences are used extensively for their high speed and security level and less errors. As a branch, the cyclotomic sequences and the generalized ones are studied widely because of their simple mathematical structures and excellent pseudo-random properties. In 1998, Ding and Helleseth introduced a new generalized cyclotomy which includes the classical cyclotomy as a special case. In this paper, based on the generalized cyclotomy, new generalized cyclotomic sequences with order two and length pq are constructed. An equivalent definition of the sequences is deduced so that the autocorrelation values of these sequences can be determined conveniently. The construction contributes to the understanding of the periodic autocorrelation structure of cyclotomically-constructed binary sequences, and the autocorrelation function takes on only a few values.
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This work is supported by the National Natural Science Foundation of China (Grant No. 60473028). The research of the second author is also supported in part by the Natural Science Foundation of Fujian Province of China (Grant No. A0540011) and the Science and Technology Foundation of Putian City (Grant No. 2005S04).
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Li, SQ., Chen, ZX., Fu, XT. et al. Autocorrelation Values of New Generalized Cyclotomic Sequences of Order Two and Length pq . J. Comput. Sci. Technol. 22, 830–834 (2007). https://doi.org/10.1007/s11390-007-9099-2
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DOI: https://doi.org/10.1007/s11390-007-9099-2