Nearly perfect sequences with arbitrary out-of-phase autocorrelation

2014/08/28 by Oğuz Yayla, Yayla, Oğuz
Computer Science · Mathematics · #05B10 #94A55 #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #math.CO #math.IT #msc:05B10 #msc:94A55

paper · pdf · doi:10.48550/arxiv.1408.6883

18 pages

arxiv created 2014/09/02 · arxiv updated 2014/09/03

Abstract

In this paper we study nearly perfect sequences (NPS) via their connection to direct product difference sets (DPDS). We prove the connection between a p-ary NPS of period n and type γ and a cyclic (n,p,n,(n-γ)/(p)+γ,0,(n-γ)/(p))-DPDS for an arbitrary integer γ. Next, we present the necessary conditions for the existence of a p-ary NPS of type γ. We apply this result for excluding the existence of some p-ary NPS of period n and type γ for n ≤ 100 and \vert γ\vert ≤ 2. We also prove the similar results for an almost p-ary NPS of type γ. Finally, we show the non-existence of some almost p-ary perfect sequences by showing the non-existence of equivalent cyclic relative difference sets by using the notion of multipliers.

Related

• Almost p-ary Sequences
• Partial direct product difference sets and sequences with ideal autocorrelation
• On a Connection between Ideal Two-level Autocorrelation and Almost Balancedness of p-ary Sequences
• On the Nonexistence of the Ding-Helleseth-Martinsens Constructions of Almost Difference Set for Cyclotomic Classes of Order 6
• On a Class of Almost Difference Sets Constructed by Using the Ding-Helleseth-Martinsens Constructions