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.

引用

页码：361 / 376

页数：16

共 50 条

[41] Value sets of some polynomials over finite fields GF(22m) [J].

Cusick, TW .

SIAM JOURNAL ON COMPUTING, 1998, 27 (01) :120-131

[42] Sequences with almost perfect linear complexity profiles and curves over finite fields [J].

Xing, CP ;

Lam, KY .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1999, 45 (04) :1267-1270

[43] ON POINT SETS IN VECTOR SPACES OVER FINITE FIELDS THAT DETERMINE ONLY ACUTE ANGLE TRIANGLES [J].

Shparlinski, Igor E. .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2010, 81 (01) :114-120

[44] An iterative algorithm for parametrization of shortest length linear shift registers over finite chain rings [J].

Kuijper, M. ;

Pinto, R. .

DESIGNS CODES AND CRYPTOGRAPHY, 2017, 83 (02) :283-305

[45] An iterative algorithm for parametrization of shortest length linear shift registers over finite chain rings [J].

M. Kuijper ;

R. Pinto .

Designs, Codes and Cryptography, 2017, 83 :283-305

[46] Subrings of p-power index in endomorphism rings of simple abelian varieties over finite fields [J].

Bradford, Jeremy .

JOURNAL OF NUMBER THEORY, 2014, 141 :159-183

[47] Space-Time Convolutional Codes over Finite Fields and Rings for Systems with Large Diversity Order [J].

Mario de Noronha-Neto ;

B. F. Uchôa-Filho .

EURASIP Journal on Wireless Communications and Networking, 2008

[48] Implicit functions over finite fields and their applications to good cryptographic functions and linear codes ☆,☆☆ [J].

Yuan, Mu ;

Qu, Longjiang ;

Li, Kangquan ;

Wang, Xiaoqiang .

FINITE FIELDS AND THEIR APPLICATIONS, 2025, 103

[49] Average Throughput with Linear Network Coding over Finite Fields: The Combination Network Case [J].

Ali Al-Bashabsheh ;

Abbas Yongacoglu .

EURASIP Journal on Wireless Communications and Networking, 2008

[50] Approximation of vectorial functions over finite fields and their restrictions to linear manifolds by affine analogues [J].

Ryabov, Vladimir G. .

DISCRETE MATHEMATICS AND APPLICATIONS, 2023, 33 (06) :387-403

← 1 2 3 4 5 →