Partial direct product difference sets and almost quaternary sequences

Date

2021-01-01

Author

Özden, Büşra
Yayla, Oğuz

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In this paper, we study the m-ary sequences with (non-consecutive) two zero-symbols and at most two distinct autocorrelation coefficients, which are known as almost m-ary nearly perfect sequences. We show that these sequences are equivalent to P-partial direct product difference sets (PDPDS), then we extend known results on the sequences with two consecutive zero symbols to non-consecutive case. Next, we study the notion of multipliers and orbit combination for P-PDPDS. Finally, we present two construction methods for a family of almost quaternary sequences with at most two out-of-phase autocorrelation coefficients.

Subject Keywords

Nearly perfect sequence, partial direct product difference set, quaternary sequence, autocorrelation, cyclotomic classes, BALANCED BINARY SEQUENCES, AUTOCORRELATION, PERFECT, FAMILY

URI

https://hdl.handle.net/11511/94878

Journal

ADVANCES IN MATHEMATICS OF COMMUNICATIONS

DOI

https://doi.org/10.3934/amc.2021010

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

B. Özden and O. Yayla, “Partial direct product difference sets and almost quaternary sequences,” ADVANCES IN MATHEMATICS OF COMMUNICATIONS, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/94878.