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Almost p-ary sequences
Date
2020-11-01
Author
Ozden, Busra
Yayla, Oğuz
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In this paper we study almost p-ary sequences and their autocorrelation coefficients. We first study the number l of distinct out-of-phase autocorrelation coefficients for an almost p-ary sequence of period n + s with s consecutive zero-symbols. We prove an upper bound and a lower bound on l. It is shown that l can not be less than min{s,p,n}. In particular, it is shown that a nearly perfect sequence with at least two consecutive zero symbols does not exist. Next we define a new difference set, partial direct product difference set (PDPDS), and we prove the connection between an almost p-ary nearly perfect sequence of type (gamma(1), gamma(2)) and period n + 2 with two consecutive zero-symbols and a cyclic (n+2,p,n,n-gamma 2-2p+gamma 2,0,n-gamma 1-1p+gamma 1,n-gamma 2-2p,n-gamma 1-1p) PDPDS for arbitrary integers gamma(1) and gamma(2). Then we prove a necessary condition on gamma(2) for the existence of such sequences. In particular, we show that they do not exist for gamma(2) <= - 3.
Subject Keywords
Computer Networks and Communications
,
Computational Theory and Mathematics
,
Applied Mathematics
URI
https://hdl.handle.net/11511/69842
Journal
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
DOI
https://doi.org/10.1007/s12095-020-00423-5
Collections
Graduate School of Applied Mathematics, Article
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B. Ozden and O. Yayla, “Almost p-ary sequences,”
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
, pp. 1057–1069, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/69842.