Period sets of linear recurrences over finite fields and related commutative rings

被引：0
|
作者：
Bush, Michael R. [1 ]
Quijada, Danjoseph [2 ]
机构：
[1] Washington & Lee Univ, Dept Math, Lexington, VA 24450 USA
[2] Univ Southern Calif, Dept Math, Los Angeles, CA 90007 USA
来源：
INVOLVE, A JOURNAL OF MATHEMATICS | 2021年 / 14卷 / 03期
关键词：
sequence; linear recurrence; period; characteristic polynomial; finite field; finite commutative ring; cyclic group algebra; SEQUENCES;
D O I：
10.2140/involve.2021.14.361
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
After giving an overview of the existing theory regarding the periods of sequences defined by linear recurrences over finite fields, we give explicit descriptions of the sets of periods that arise if one considers all sequences over F-q generated by linear recurrences for a fixed choice of the degree k in the range 1 <= k <= 4. We also investigate the periods of sequences generated by linear recurrences over rings of the form F-q1 circle plus ... circle plus F-qr.
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页码：361 / 376
页数：16
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