<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><msub><mrow><mi mathvariant="bold">ℤ</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/749C61A3-9027-4a35-96DD-7350B25D517F-M001.jpg"><?fx-imagestate width="5.58799982" height="5.67266655"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/749C61A3-9027-4a35-96DD-7350B25D517F-M001c.jpg"><?fx-imagestate width="5.58799982" height="5.67266655"?></graphic></alternatives></inline-formula>上LCD循环码及其二元像

开晓山; 廖文敬

doi:10.12263/DZXB.20200588

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上LCD循环码及其二元像

科研通信 | 更新时间：2025-12-08

- $ℤ_{4}$ 上LCD循环码及其二元像
- LCD Cyclic Codes over ℤ₄ and Binary Images
- 电子学报 2021年49卷第11期页码：2284-2288
- 作者机构：
  
  合肥工业大学数学学院，安徽合肥 230601
- 作者简介：
  
  [ "开晓山（通信作者）　男，1975年生，安徽青阳人. 合肥工业大学数学学院教授，博士生导师，研究方向为编码理论与信息安全.E-mail:kxs6@sina.com" ]
  [ "廖文敬　女，1996年生，安徽宿州人. 合肥工业大学硕士研究生，主要研究方向为代数编码. E-mail:1846755441@qq.com" ]
- 基金信息：
  
  国家自然科学基金(61972126;61772168;61802102);中央高校基本科研业务费专项资金(PA2019GDZC0097)
- DOI：10.12263/DZXB.20200588
  中图分类号： TN911.22
- 收稿：2020-06-17，
  
  修回：2021-05-23，
  
  纸质出版：2021-11-25
- 稿件说明：
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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.

ℤ_{4}

上LCD循环码及其二元像

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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

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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 .

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ℤ4上LCD循环码及其二元像

LCD Cyclic Codes over ℤ4 and Binary Images

DOI：10.12263/DZXB.20200588

摘要

Abstract

关键词

Keywords

references

$ℤ_{4}$ 上LCD循环码及其二元像

LCD Cyclic Codes over ℤ₄ and Binary Images