Abstract
Let \(p\) and \(q\) be two odd primes with \(p=Mf+1\) and \(M\) is even. A new construction of \(M\)-ary sequences of period \(pq\) with low periodic autocorrelation is presented in this paper based on interleaving the \(M\)-ary power residue sequence of period \(p\) according to the quadratic residue with respect to \(q\). This construction can generate the well-known twin-prime sequence and generalized cyclotomy sequence of order two if \(M=2\). For \(M=4\), a new class of quaternary sequences of period \(pq\) with maximal nontrivial autocorrelation value being either \(\sqrt{5}\) or \(3\) is obtained. This achieves the best known results for such kind of quaternary sequences.
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Acknowledgments
The authors would like to thank the referees for their comments that improved the presentation and quality of this paper. This work of N. Li and X. Tang was supported by in part by the Scientific Research Foundation for Returned Scholars, Chinese Ministry of Education, the key grant Project of Chinese Ministry of Education under Grant 311031, and the funds for the Excellent Ph.D. Dissertation of Southwest Jiaotong University. The work of T. Helleseth was supported in part by the Norwegian Research Council, and High-End Foreign-Expert Program, State Administration of Foreign Experts Affairs, China.
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Communicated by J. Jedwab.
N. Li is currently a visiting Ph.D. student (Sept. 2011–Aug. 2013) in the Department of Informatics, University of Bergen.
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Li, N., Tang, X. & Helleseth, T. New \(M\)-ary sequences with low autocorrelation from interleaved technique. Des. Codes Cryptogr. 73, 237–249 (2014). https://doi.org/10.1007/s10623-013-9821-8
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DOI: https://doi.org/10.1007/s10623-013-9821-8