A Note on Skew Cyclic Codes over a Class of Rings

被引：0

作者：

Hai Q Dinh ^{[1
,2
]}

Bac T Nguyen ^{[3
]}

Sriboonchitta, Songsak ^{[4
]}

机构：

[1] Ton Duc Thang Univ, Inst Computat Sci, Div Computat Math & Engn, Ho Chi Minh City, Vietnam

[2] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

[3] Thai Nguyen Univ, Univ Econ & Business Adm, Dept Basic Sci, Thai Nguyen, Thai Nguyen Pro, Vietnam

[4] Chiang Mai Univ, Fac Econ, Ctr Excellence Econometr, Chiang Mai 52000, Thailand

来源：

ALGEBRA COLLOQUIUM | 2020年 / 27卷 / 04期

关键词：

skew constacyclic codes; dual codes; repeated-root codes; quasi-cyclic codes; local rings;

D O I：

10.1142/S1005386720000589

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study skew cyclic codes over a class of rings R = F-0 circle plus F-1 circle plus ...circle plus Ft-1, where each F-1 (i = 0, . . . , t - 1) is a finite field. We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R. Moreover, we discuss possible extension of our results in the more general setting of delta(R)-dual skew constacyclic codes over R, where delta(R) is an automorphism of R.

引用

页码：703 / 712

页数：10

共 50 条

[1] Skew quasi-cyclic codes over Galois rings
Bhaintwal, Maheshanand
DESIGNS CODES AND CRYPTOGRAPHY, 2012, 62 (01) : 85 - 101
[2] Studies on Two Classes of Skew Cyclic Codes Over Rings
Li, Yan
Li, Xiuli
INFORMATION TECHNOLOGY AND INTELLIGENT TRANSPORTATION SYSTEMS, VOL 1, 2017, 454 : 95 - 101
[3] Skew quasi-cyclic codes over Galois rings
Maheshanand Bhaintwal
Designs, Codes and Cryptography, 2012, 62 : 85 - 101
[4] Skew Codes over Rings
Abualrub, Taher
Seneviratne, Padmapani
INTERNATIONAL MULTICONFERENCE OF ENGINEERS AND COMPUTER SCIENTISTS (IMECS 2010), VOLS I-III, 2010, : 846 - 847
[5] ON QUANTUM CODES FROM CYCLIC CODES OVER A CLASS OF NONCHAIN RINGS
Sari, Mustafa
Siap, Irfan
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2016, 53 (06) : 1617 - 1628
[6] Quantum Codes from Cyclic Codes over A Class of Nonchain Rings
Sari, Mustafa
Siap, Irfan
2015 6TH INTERNATIONAL CONFERENCE ON MODELING, SIMULATION, AND APPLIED OPTIMIZATION (ICMSAO), 2015,
[7] Idempotents in simple skew group rings and applications to skew cyclic codes
El Badry, Mohammed
Haily, Abdelfattah
Mounir, Ayoub
COMMUNICATIONS IN ALGEBRA, 2024, 52 (01) : 305 - 314
[8] Skew constacyclic codes over Galois rings
Boucher, Delphine
Sole, Patrick
Ulmer, Felix
ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2008, 2 (03) : 273 - 292
[9] Codes as Modules over Skew Polynomial Rings
Boucher, Delphine
Ulmer, Felix
CRYPTOGRAPHY AND CODING, PROCEEDINGS, 2009, 5921 : 38 - +
[10] A class of skew cyclic codes and application in quantum codes construction
Dinh, Hai Q.
Bag, Tushar
Upadhyay, Ashish K.
Bandi, Ramakrishna
Tansuchat, Roengchai
DISCRETE MATHEMATICS, 2021, 344 (02)

← 1 2 3 4 5 →