LCD Cyclic Codes over ℤ<sub>4</sub> and Binary Images

KAI Xiao-shan; LIAO Wen-jing

doi:10.12263/DZXB.20200588

您当前的位置：

首页 >

文章列表页 >

LCD Cyclic Codes over ℤ₄ and Binary Images

CORRESPONDENCE | 更新时间：2025-12-08

- LCD Cyclic Codes over ℤ₄ and Binary Images
- ACTA ELECTRONICA SINICA Vol. 49, Issue 11, Pages: 2284-2288(2021)
- 作者机构：
  
  合肥工业大学数学学院，安徽合肥 230601
- 作者简介：
- 基金信息：
- DOI：10.12263/DZXB.20200588
  CLC： TN911.22
- Received：17 June 2020，
  
  Revised：2021-05-23，
  
  Published：25 November 2021
- 稿件说明：
移动端阅览
开晓山,廖文敬.ℤ4上LCD循环码及其二元像[J].电子学报,2021,49(11):2284-2288.

KAI Xiao-shan,LIAO Wen-jing.LCD Cyclic Codes over ℤ₄ and Binary Images[J].ACTA ELECTRONICA SINICA,2021,49(11):2284-2288.
开晓山,廖文敬.ℤ4上LCD循环码及其二元像[J].电子学报,2021,49(11):2284-2288. DOI： 10.12263/DZXB.20200588.

KAI Xiao-shan,LIAO Wen-jing.LCD Cyclic Codes over ℤ₄ and Binary Images[J].ACTA ELECTRONICA SINICA,2021,49(11):2284-2288. DOI： 10.12263/DZXB.20200588.

摘要

循环码和线性互补对偶（LCD）码是两类重要的线性码，在数据存储、通信系统和密码等领域有着广泛的应用. 本文研究了

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951007&type=

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951004&type=

3.13266683

3.21733332

上奇长度的LCD循环码，给出了

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951007&type=

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951004&type=

3.13266683

3.21733332

上奇长度的循环码为LCD码的一个充要条件，证明了

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951007&type=

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951004&type=

3.13266683

3.21733332

上LCD循环码的二元像是可逆码；构造了

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951007&type=

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951004&type=

3.13266683

3.21733332

上长为

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43950996&type=

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951009&type=

8.55133343

2.53999996

的LCD循环码，得到了参数较好的二元非线性可逆码.

Abstract

Cyclic codes and linear complementary dual (LCD) codes are two important classes of linear codes which have been extensively used in data storage systems

communication systems and cryptography. In this paper

LCD cyclic codes over

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951007&type=

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951004&type=

3.13266683

3.21733332

of odd length are explored. A sufficient and necessary condition is given for cyclic codes over

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951007&type=

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951004&type=

3.13266683

3.21733332

of odd length to be LCD. It is proved that the binary images of LCD cyclic codes over

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951007&type=

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951004&type=

3.13266683

3.21733332

are reversible codes. LCD cyclic codes over

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951007&type=

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951004&type=

3.13266683

3.21733332

of length

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43950996&type=

http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43951009&type=

8.55133343

2.53999996

are constructed. And binary nonlinear reversible codes with good parameters are obtained.

关键词

Keywords

references

Massey J L . Linear codes with complementary duals [J]. Discrete Mathematics , 1992 , 106 ( 107 ): 337 - 342 .

Carlet C , Guilley S . Complementary dual codes for counter-measures to side-channel attacks [A]. The 4th International Castle Meeting Coding Theory and Applications [C]. Palmela Castle, Portugal : Springer , 2015 . 97 - 105 .

Beelen P , Jin L . Explicit MDS codes with complementary duals [J]. IEEE Transactions on Information Theory , 2018 , 64 ( 11 ): 7188 - 7193 .

Carlet C , Mesnager S , Tang C , Qi Y . Euclidean and Hermitian LCD MDS codes [J]. Designs , Codes and Cryptography, 2018 , 86 ( 11 ): 2606 - 2618 .

钱毅 , 李平 , 唐永生 . 一种四元厄米特LCD码与厄米特自正交码的构造方法 [J]. 电子学报 , 2020 , 48 ( 3 ): 577 - 581 .

Qian Y , Li P , Tang Y S . A construction method of quaternary Hermitian LCD codes and Hermitian self-orthogonal codes [J]. Acta Electronica Sinica , 2020 , 48 ( 3 ): 577 - 581 . (in Chinese)

Carlet C , Mesnager S , Tang C , et al . Linear codes over <math id="M468"><msub><mrow><mi mathvariant="normal">𝔽</mi></mrow><mrow><mi>q</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43954277&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43954270&type= 2.87866688 3.21733332 are equivalent to LCD codes for <math id="M469"><mi>q</mi><mo>></mo><mn mathvariant="normal">3</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43954281&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43954278&type= 6.77333355 2.96333337 [J]. IEEE Transactions on Information Theory , 2018 , 64 ( 4 ): 3010 - 3017 .

Liu X , Liu H . LCD codes over ﬁnite chain rings [J]. Finite Fields and Their Applications , 2015 , 34 ( 7 ): 1 - 19 .

Shi M , Zhu H , Qian L , et al . On self-dual and LCD double circulant and double negacirculant codes over <math id="M470"><msub><mrow><mi mathvariant="normal">𝔽</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>+</mo><mi>u</mi><msub><mrow><mi mathvariant="normal">𝔽</mi></mrow><mrow><mi>q</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43954286&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43954291&type= 11.34533310 3.21733332 [J]. Cryptography and Communications , 2020 , 12 ( 1 ): 53 - 70 .

Liu Z , Wang J . Linear complementary dual codes over rings [J]. Designs , Codes and Cryptography, 2019 , 87 ( 11 ): 3077 - 3086 .

Alahmadi A , Alhazmi H , Helleseth T , et al . On the lifted Melas code [J]. Cryptography and Communications , 2016 , 8 ( 1 ): 7 - 18 .

Yang X , Massey J L . The necessary and sufficient condition for a cyclic code to have a complementary dual [J]. Discrete Mathematics , 1994 , 126 ( 3 ): 391 - 393 .

Li C , Ding C , Li S . LCD cyclic codes over ﬁnite ﬁelds [J]. IEEE Transactions on Information Theory , 2017 , 63 ( 7 ) : 4344 - 4356 .

Wan Z . Quaternary Codes [M]. Singapore : World Scientiﬁc , 1997 .

Norton G H , Salagean A . On the Hamming distance of linear codes over a finite chain ring [J]. IEEE Transactions on Information Theory , 2000 , 46 ( 3 ): 1060 - 1067 .

Norton G H , Salagean A . On the structure of linear and cyclic codes over a ﬁnite chain ring [J]. Applicable Algebra in Engineering , Communication and Computing, 2000 , 10 ( 7 ): 489 - 506 .

Wolfmann J . Binary images of cyclic codes over <math id="M471"><msub><mrow><mi mathvariant="bold">ℤ</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43954297&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=43954295&type= 3.13266683 3.21733332 [J]. IEEE Transactions on Information Theory , 2001 , 47 ( 5 ): 1773 - 1779 .

MacWilliams F J , Sloane N J A . The Theory of Error-Correcting Codes [M]. Amsterdam, Netherland : North-Holland Publishing Company , 1977 .

Grassl M . Bounds on the minimum distance of linear codes and quantum codes [N]. http: // www. codetables.de http://www.codetables.de , 2020-06-15 .

Interlando J C , Palazzo R , Elia M . On the decoding of Reed-Solomon and BCH codes over integer residue rings [J]. IEEE Transactions on Information Theory , 1997 , 43 ( 3 ): 1013 - 1021 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

A New Method on the Construction of Optimal Codes over Finite Field

MacWilliams Identities of Linear Codes Over Ring Z₄ with Respect to the RT Metric

Several Weight Enumerators of Linear Codes and Their MacWilliams Identities over Ring F_p+vF_p+v²F_p

Upper Bounds on the Length of Linear Unequal Error Protection Codes and Its Application

Related Author

LI Hong-ju

DING Jian

SHI Min-jia

XU He-qian

ZHU Shi-xin

LI Ping

ZHU Shi-xin

WU Bo

Related Institution

Department of Common Course, Anhui Xinhua University

School of Mathematics SciencesAnhui UniversityHefeiAnhui China

Department of MathematicsHefei Teachers CollegeHefeiAnhui 230601China

Department of MathematicsHefei University of TechnologyHefeiAnhui 230009China

School of Mathematics Sciences,Anhui University

⁰

LCD Cyclic Codes over ℤ4 and Binary Images

DOI：10.12263/DZXB.20200588

摘要

Abstract

关键词

Keywords

references

LCD Cyclic Codes over ℤ₄ and Binary Images