Almost p-Ary Perfect Sequences

  • Yeow Meng Chee
  • Yin Tan
  • Yue Zhou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6338)


A sequence a = (a 0, a 1, a 2, ⋯ , a n ) is said to be an almost p-ary sequence of period n + 1 if a 0 = 0 and \(a_i=\zeta_p^{b_i}\) for 1 ≤ i ≤ n, where ζ p is a primitive p-th root of unity and b i  ∈ {0, 1, ⋯ , p − 1}. Such a sequence a is called perfect if all its out-of-phase autocorrelation coefficients are zero; and is called nearly perfect if its out-of-phase autocorrelation coefficients are all 1, or are all − 1. In this paper, on the one hand, we construct almost p-ary perfect and nearly perfect sequences; on the other hand, we present results to show they do not exist with certain periods. It is shown that almost p-ary perfect sequences correspond to certain relative difference sets, and almost p-ary nearly perfect sequences correspond to certain direct product difference sets. Finally, two tables of the existence status of such sequences with period less than 100 are given.


almost p-ary sequences almost p-ary perfect sequences almost p-ary nearly perfect sequences relative difference set direct product difference set 


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yeow Meng Chee
    • 1
  • Yin Tan
    • 1
  • Yue Zhou
    • 2
  1. 1.Division of Mathematical Sciences, School of Physical & Mathematical SciencesNanyang Technological UniversitySingapore
  2. 2.Department of MathematicsOtto-von-Guericke-University MagdeburgMagdeburgGermany

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