Three new classes of optimal quinary cyclic codes with minimum distance four
Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an important subject of study for many years. Recently, several classes of optimal quinary cyclic codes of the forms C ( 0 , 1 , e ) and C ( 1 , e , s ) are presented in the...
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| Published in | Applicable algebra in engineering, communication and computing Vol. 36; no. 3; pp. 493 - 501 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.05.2025
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0938-1279 1432-0622 |
| DOI | 10.1007/s00200-023-00621-7 |
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| Abstract | Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an important subject of study for many years. Recently, several classes of optimal quinary cyclic codes of the forms
C
(
0
,
1
,
e
)
and
C
(
1
,
e
,
s
)
are presented in the literature, where
s
=
5
m
-
1
2
and
2
≤
e
≤
5
m
-
2
. In this paper, by considering the solutions of certain equations over finite fields, we give three new classes of infinite families of optimal quinary cyclic codes of the form
C
(
1
,
e
,
s
)
with parameters
[
5
m
-
1
,
5
m
-
2
m
-
2
,
4
]
. Specifically, we make progress towards an open problem proposed by Gaofei Wu et al. [
17
]. |
|---|---|
| AbstractList | Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an important subject of study for many years. Recently, several classes of optimal quinary cyclic codes of the forms
C
(
0
,
1
,
e
)
and
C
(
1
,
e
,
s
)
are presented in the literature, where
s
=
5
m
-
1
2
and
2
≤
e
≤
5
m
-
2
. In this paper, by considering the solutions of certain equations over finite fields, we give three new classes of infinite families of optimal quinary cyclic codes of the form
C
(
1
,
e
,
s
)
with parameters
[
5
m
-
1
,
5
m
-
2
m
-
2
,
4
]
. Specifically, we make progress towards an open problem proposed by Gaofei Wu et al. [
17
]. Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an important subject of study for many years. Recently, several classes of optimal quinary cyclic codes of the forms C(0,1,e) and C(1,e,s) are presented in the literature, where s=5m-12 and 2≤e≤5m-2. In this paper, by considering the solutions of certain equations over finite fields, we give three new classes of infinite families of optimal quinary cyclic codes of the form C(1,e,s) with parameters [5m-1,5m-2m-2,4]. Specifically, we make progress towards an open problem proposed by Gaofei Wu et al. [17]. |
| Author | Liu, Yan Cao, Xiwang |
| Author_xml | – sequence: 1 givenname: Yan surname: Liu fullname: Liu, Yan email: liuyan0916@126.com organization: College of Mathematics and Physics, Yancheng Institute of Technology – sequence: 2 givenname: Xiwang surname: Cao fullname: Cao, Xiwang organization: School of Mathematical Sciences, Nanjing University of Aeronautics and Astronautics, Key Laboratory of Mathematical Modeling and High Performance Computing of Air Vehicles(NUAA), MIIT |
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| Cites_doi | 10.1016/j.ffa.2018.08.004 10.1016/j.ffa.2013.08.005 10.1109/LCOMM.2020.2983373 10.1016/j.ffa.2015.10.004 10.1017/CBO9780511807077 10.1007/s10623-019-00679-w 10.1016/j.ffa.2016.03.007 10.1049/cje.2020.02.011 10.1109/TIT.2015.2451657 10.1109/IWSDA.2015.7458415 10.1016/j.ffa.2019.07.002 10.1007/s00200-021-00489-5 10.3934/amc.2021033 10.1109/TIT.2005.847722 10.1109/TIT.2013.2260795 10.1016/j.disc.2018.01.003 10.1007/s12095-015-0159-0 10.1016/j.ffa.2021.101898 10.1016/j.ffa.2014.06.001 10.1016/j.ffa.2020.101671 10.1109/LCOMM.2019.2921330 |
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| Copyright | The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. |
| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. – notice: The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. |
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| Keywords | 94B15 Quinary code Minimum distance Optimal code Cyclic code 11T71 |
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| References | 621_CR9 H Yan (621_CR20) 2018; 54 Z Zhou (621_CR23) 2014; 25 Y Tian (621_CR15) 2017; 38 D Liao (621_CR10) 2019; 23 C Carlet (621_CR1) 2005; 51 J Fan (621_CR4) 2020; 29 L Wang (621_CR16) 2016; 40 W Huffman (621_CR6) 2003 D Han (621_CR5) 2019; 59 G Xu (621_CR19) 2016; 8 Y Liu (621_CR12) 2023; 34 Z Zha (621_CR22) 2020; 64 L Lan (621_CR7) 2018; 341 621_CR17 C Ding (621_CR2) 2013; 59 C Fan (621_CR3) 2016; 37 Y Liu (621_CR13) 2020; 88 Z Zha (621_CR21) 2021; 75 N Li (621_CR8) 2014; 30 Y Liu (621_CR11) 2020; 24 M Xiong (621_CR18) 2015; 61 Y Liu (621_CR14) 2023; 17 |
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| SubjectTerms | Artificial Intelligence Codes Communications systems Computer Hardware Computer Science Data storage Fields (mathematics) Original Paper Storage systems Symbolic and Algebraic Manipulation Theory of Computation |
| Title | Three new classes of optimal quinary cyclic codes with minimum distance four |
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