AAECC (2010) 21:417–441 DOI 10.1007/s00200-010-0131-3 On the generalized large set of Kasami sequences Wenfeng Jiang · Lei Hu · Xiangyong Zeng Received: 11 October 2009 / Revised: 7 September 2010 / Published online: 23 September 2010 © Springer-Verlag 2010 Abstract In this paper, we present a new family of binary Kasami sequences of length 2 n - 1 for even integer n = 2m. It generalizes the recently proposed large set 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 ± 2 m , -1 ± 2 m+gcd(m,l ) , and has family size 2 3m + 2 m or 2 3m + 2 m - 1. We also completely determine the distribution of these correlation values. Keywords Binary sequence family · Kasami sequence · Quadratic form 1 Introduction Sequence families with low correlation play an important role in many appli- cation areas such as code division multiple access (CDMA) communication and cryptography [14, 4]. 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). W. Jiang (B ) · L. Hu State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, 100049 Beijing, China e-mail: wfjiang@is.ac.cn L. Hu e-mail: hu@is.ac.cn X. Zeng Faculty of Mathematics and Computer Science, Hubei University, 430062 Wuhan, China e-mail: xzeng@hubu.edu.cn 123