A Family of Binary Sequences with 4-Valued Optimal Out-of-Phase Correlation and Large Linear Span*This work is supported in part by the National Science Foundation of China (NSFC) under Grants No.60373041 and No.90104034, and in part by the open foundation of the State Key Laboratory of Information Security.

  • Authors:

  • Xiangyong Zeng;Lei Hu;Wenfeng Jiang

  • Affiliations:

  • The authors are with the Faculty of Mathematics and Computer Science, Hubei University, Wuhan, 430062, China. E-mail: xzeng@hubu.edu.cn,;The authors are with the State Key Laboratory of Information Security (Graduate School of Chinese Academy of Sciences), 19A Yuquan Road, Beijing, 100049, China. E-mail: hu@is.ac.cn;The authors are with the Faculty of Mathematics and Computer Science, Hubei University, Wuhan, 430062, China. E-mail: xzeng@hubu.edu.cn,

  • Venue:
  • IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
  • Year:
  • 2006

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Abstract

In this paper, a new family (r) of 2n binary sequences of period 2n-1 is proposed, where n≡2 mod 4 and gcd (r, 2n/2-1)=1. The presented family takes 4-valued out-of-phase auto- and cross-correlation values -1, ±2n/2-1, and 2n/2+1-1, and its correlation distribution is determined. For r=2(n-2)/4-1, each sequence in (r), except the unique ideal autocorrelation sequence in the family, is proved to have a large linear span n·2n/2-2, whilst the linear span of the latter is n · 2(n-2)/4-1.