Occurrence indices of elements in linear recurrence sequences over primary residue rings

Occurrence indices of elements in linear recurrence sequences over primary residue rings We study distances to the first occurrence (occurrence indices) of a given element in a linear recurrence sequence over a primary residue ring $$ \mathbb{Z}_{p^n } $$ . 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 $$ \mathbb{Z}_{p^n } $$ , 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Occurrence indices of elements in linear recurrence sequences over primary residue rings

Loading next page...
 
/lp/springer_journal/occurrence-indices-of-elements-in-linear-recurrence-sequences-over-wpNjvuwiv1
Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2008 by Pleiades Publishing, Ltd.
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946008020087
Publisher site
See Article on Publisher Site

Abstract

We study distances to the first occurrence (occurrence indices) of a given element in a linear recurrence sequence over a primary residue ring $$ \mathbb{Z}_{p^n } $$ . 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 $$ \mathbb{Z}_{p^n } $$ , 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.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 11, 2008

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from
Google Scholar,
PubMed
Create lists to
organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off