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Optimal frequency-hopping sequences based on the decimated m-sequences

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Abstract

Let an \((n,l,\lambda )\)-FHS denote a frequency-hopping sequence of length n over an alphabet with size l with maximum periodic Hamming out-of-phase autocorrelation \(\lambda\) and let q be a power of a prime. In 2009, Ge, Miao and Yao constructed a family of optimal \((\frac{q^m-1}{e},q,\frac{q^{m-1}-1}{e})\)-FHSs achieving the Lempel-Greenberger bound based on the e-decimation of an m-sequence, where \(e|(q-1)\) and \(\gcd {(e,m)}=1\). Inspired by their work, we improve the results about the alphabet size of this family of FHSs and obtain some optimal FHSs with new parameters by virtue of character sums over finite fields.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11771007) and was also supported by the Funding of Nanjing Institute of Technology (Grant No. ZKJ201909 and QKJ201804).

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Authors and Affiliations

  1. College of Liberal Arts and Science, National University of Defense Technology, Changsha, 410073, P.R. China

    Shanding Xu

  2. Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing, 211167, P.R. China

    Shanding Xu

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Correspondence to Shanding Xu.

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Xu, S. Optimal frequency-hopping sequences based on the decimated m-sequences. Cryptogr. Commun. 14, 983–998 (2022). https://doi.org/10.1007/s12095-022-00569-4

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