NEARLY PERFECT SEQUENCES WITH ARBITRARY OUT-OF-PHASE AUTOCORRELATION

Date

2016-05-01

Author

Yayla, Oğuz

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A sequence of period n is called a nearly perfect sequence of type gamma if all out-of-phase autocorrelation coefficients are a constant gamma. 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 gamma and a cyclic (n,p,n, n-gamma/p + gamma, 0, n-gamma/p)-DPDS for an arbitrary integer gamma. Next, we present the necessary conditions for the existence of a p-ary NPS of type gamma. We apply this result for excluding the existence of some p-ary NPS of period n and type gamma for n <= 100 and vertical bar gamma vertical bar <= 2. We also prove the similar results for an almost p-ary NPS of type gamma. 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.

URI

https://hdl.handle.net/11511/69845

Journal

ADVANCES IN MATHEMATICS OF COMMUNICATIONS

DOI

https://doi.org/10.3934/amc.2016014

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

O. Yayla, “NEARLY PERFECT SEQUENCES WITH ARBITRARY OUT-OF-PHASE AUTOCORRELATION,” ADVANCES IN MATHEMATICS OF COMMUNICATIONS, pp. 401–411, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/69845.