Abstract:
We study distances to the first occurrence (occurrence indices) of a given element in a linear recurrence sequence over a primary residue ring Zpn. We give conditions on the characteristic polynomial F(x) of a linear recurrence sequence u which guarantee that all elements of the ring occur in u. For the case where F(x) is a reversible Galois polynomial over Zpn, we give upper bounds for occurrence indices of elements in a linear recurrence sequence u. A situation where the characteristic polynomial F(x) of a linear recurrence sequence u is a trinomial of a special form over Z4 is considered separately. In this case we give tight upper bounds for occurrence indices of elements of u.
Citation:
D. N. Bylkov, O. V. Kamlovskii, “Occurrence Indices of Elements in Linear Recurrence Sequences over Primary Residue Rings”, Probl. Peredachi Inf., 44:2 (2008), 101–109; Problems Inform. Transmission, 44:2 (2008), 161–168
\Bibitem{BylKam08}
\by D.~N.~Bylkov, O.~V.~Kamlovskii
\paper Occurrence Indices of Elements in Linear Recurrence Sequences over Primary Residue Rings
\jour Probl. Peredachi Inf.
\yr 2008
\vol 44
\issue 2
\pages 101--109
\mathnet{http://mi.mathnet.ru/ppi1274}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2435243}
\transl
\jour Problems Inform. Transmission
\yr 2008
\vol 44
\issue 2
\pages 161--168
\crossref{https://doi.org/10.1134/S0032946008020087}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-48249156609}
Linking options:
https://www.mathnet.ru/eng/ppi1274
https://www.mathnet.ru/eng/ppi/v44/i2/p101
This publication is cited in the following 3 articles:
Qun-Xiong Zheng, Dongdai Lin, Wen-Feng Qi, Lecture Notes in Computer Science, 11449, Information Security and Cryptology, 2019, 568
Yuan Cheng, Wen-Feng Qi, Qun-Xiong Zheng, Dong Yang, “On the distinctness of primitive sequences over Z/(p e q) modulo 2”, Cryptogr. Commun., 8:3 (2016), 371
O. V. Kamlovskii, “Kolichestvo razlichnykh multigramm v lineinykh rekurrentnykh posledovatelnostyakh nad koltsami Galua”, Matem. vopr. kriptogr., 4:3 (2013), 49–82