New construction for binary sequences of period pm - 1 with optimal autocorrelation using (z + 1)d + azd + b

Jong Seon No, Habong Chung, Hong-Yeop Song, Kyeongcheol Yang, Jung Do Lee, Tor Helleseth

Research output: Contribution to journalLetter

23 Citations (Scopus)


In this correspondence, we present a construction for binary sequences (s(t)) of period N = pm - 1 for an odd prime p based on the polynomial (z + 1)d + azd + b, and discuss them in some cases of parameters p, m, d, a, and b. We show that new sequences from our construction are balanced or almost balanced and have optimal three-level autocorrelation for the case when the polynomial (z + 1)d + zd + a can be transformed into the form z2 - c. We also derive the distribution of autocorrelation values they take on. The sequences satisfy constant-on-the-coset property, and we will show that there are more than one characteristic phases with constant-on-the-coset property. Some other interesting properties of these sequences will be presented. For the cases when the polynomial (z + 1)d + zd + a cannot be transformed into the form z2 - c, we performed extensive computer search, and results are summarized. Based on these results, some open problems are formulated.

Original languageEnglish
Pages (from-to)1638-1644
Number of pages7
JournalIEEE Transactions on Information Theory
Issue number4
Publication statusPublished - 2001 Jan 1


All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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