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On the generalized large set of Kasami sequences

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Abstract

In this paper, we present a new family of binary Kasami sequences of length 2n − 1 for even integer n = 2m. It generalizes the recently proposed large set \({\mathcal{F}^{(l)}}\) of Kasami sequences by relaxing the restriction on l to a more general case. The presented sequence family takes five nontrival correlation values −1, −1 ± 2m, −1 ± 2m + gcd(m,l), and has family size 23m + 2m or 23m + 2m −1. We also completely determine the distribution of these correlation values.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, 100049, Beijing, China

    Wenfeng Jiang & Lei Hu

  2. Faculty of Mathematics and Computer Science, Hubei University, 430062, Wuhan, China

    Xiangyong Zeng

Authors
  1. Wenfeng Jiang
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  2. Lei Hu
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  3. Xiangyong Zeng
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Correspondence to Wenfeng Jiang.

Additional information

This work was partially supported by the National Science Foundation of China (NSFC) under Grants 60773134, 60973130 and 10990011, and the National Basic Research Program of China (2007CB311201). The work of X. Zeng was also supported by the Natural Science Foundation for Excellent Youth Scholars of Hubei Province of China (2009CDA147).

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Jiang, W., Hu, L. & Zeng, X. On the generalized large set of Kasami sequences. AAECC 21, 417–441 (2010). https://doi.org/10.1007/s00200-010-0131-3

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  • DOI: https://doi.org/10.1007/s00200-010-0131-3

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