Linear complementary dual codes over rings

Liu Zihui; Wang Jinliang

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Linear complementary dual codes over rings

机译：线性互补双重代码在环上

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摘要

By using linear algebra over finite commutative rings, we will present some judging criterions for linear complementary dual (LCD) codes over rings, in particular, free LCD codes over finite commutative rings are described. By using free LCD codes over finite commutative rings and the Chinese Remainder Theorem, LCD codes over semi-simple rings are constructed and the equivalence of free codes and free LCD codes is given. In addition, all the possible LCD codes over chain rings are determined. We also generalize the judging criterion for cyclic LCD codes over finite fields to cyclic LCD codes over chain rings. Based on the above results and the Chinese Remainder Theorem, we also present results for LCD codes over principal ideal rings.

机译：通过使用线性代数在有限的换向环上，我们将呈现用于线性互补双（LCD）代码的一些判断标准，特别地描述了在有限换向环上的自由LCD代码。通过使用有限的换向环和中文剩余定理的免费LCD代码，构建了半简单环上的LCD代码，并给出了免费代码和免费LCD代码的等价。此外，确定环环上的所有可能的LCD代码。我们还概括了循环LCD代码的判断标准，以在链环上的循环LCD代码上的有限字段。基于上述结果和中国剩余的定理，我们还向LCD代码提供了主要理想环的结果。

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来源
《Designs, Codes and Crytography》 |2019年第12期|3077-3086|共10页
作者
Liu Zihui; Wang Jinliang;
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作者单位

Beijing Inst Technol Dept Math Beijing 100081 Peoples R China;

Liaocheng Univ Sch Comp Sci Liaocheng 252059 Shandong Peoples R China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Principal ideal rings; Chain rings; LCD codes; Chinese Remainder Theorem; Generating polynomial;

机译：主要理想戒指;链环;液晶代码;中国剩余定理;产生多项式;

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1. The dual of a constacyclic code, self dual, reversible constacyclic codes and constacyclic codes with complementary duals over finite local Frobenius non-chain rings with nilpotency index 3 [J] . Castillo-Guillen C. A., Renteria-Marquez C., Sarmiento-Rosales E., Discrete mathematics . 2019,第8期

机译：芳基奇的代码，自我双重，可逆的芳基码代码和具有互补的双重的互补性双倍的芳基码，具有尼芯指数3
2. Modal Θ-valent linear codes with complementary modal Θ-valent duals [J] . Tsimi Jean Armand, Youdom Rose Christelle, Boakye Benjamin Journal of information and optimization sciences . 2021,第5期

机译：模态θ-Valent线性码与互补模态θ-vergy双重
3. Linear codes with complementary duals from some strongly regular subgraphs of the McLaughlin graph [J] . Leemans Dimitri, Rodrigues Bernardo Mathematical communications . 2016,第2期

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4. Linear codes with complementary duals meet the Gilbert-Varshamov bound [C] . Sendrier, N. . 2004

机译：具有互补对偶的线性代码满足Gilbert-Varshamov界
5. Weight enumerators and gray maps of linear codes over rings [D] . Yildiz, Bahattin 2006

机译：环上线性代码的权重枚举器和灰度图
6. An Interstitial 4q Deletion with a Mosaic Complementary Ring Chromosome in a Child with Dysmorphism Linear Skin Pigmentation and Hepatomegaly [O] . J. Carter, H. Brittain, D. Morrogh, 2017

机译：异型性皮肤色素沉着和肝肿大的儿童与马赛克互补环染色体间质性4q删除。
7. Linear codes with complementary duals meet the Gilbert–Varshamov bound [O] . Sendrier Nicolas 2004

机译：带有互补对偶的线性代码满足吉尔伯特-瓦尔沙莫夫界
8. Minimal trellises for linear block codes and their duals [R] . Kiely, A. B., Dolinar, S., Ekroot, L., 1995

机译：线性分组码及其对偶的最小格子

Linear complementary dual codes over rings

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