English
Related papers

Related papers: Complementary Dual Algebraic Geometry Codes

200 papers

Linear code with complementary dual($LCD$) are those codes which meet their duals trivially. In this paper we will give rather alternative proof of Massey's theorem\cite{Massey2}, which is one of the most important characterization of $LCD$…

Information Theory · Computer Science 2018-02-09 N. S. Darkunde

LCD codes are linear codes that intersect with their dual trivially. Quasi cyclic codes that are LCD are characterized and studied by using their concatenated structure. Some asymptotic results are derived. Hermitian LCD codes are…

Information Theory · Computer Science 2016-08-08 Cem Güneri , Buket Özkaya , Patrick Solé

Linear complementary dual codes (LCD) intersect trivially with their dual. In this paper, we develop a new characterization for LCD codes, which allows us to judge the complementary duality of linear codes from the codeword level. Further,…

Information Theory · Computer Science 2023-07-10 Chaofeng Guan , Ruihu Li , Zhi Ma

Linear complementary dual (LCD) codes can provide an optimum linear coding solution for the two-user binary adder channel. LCD codes also can be used to against side-channel attacks and fault non-invasive attacks. Let $d_{LCD}(n, k)$ denote…

Information Theory · Computer Science 2024-12-20 Guodong Wang , Shengwei Liu , Hongwei Liu

For a linear code $C$ over a finite field, if its dual code $C^{\perp}$ is equivalent to itself, then the code $C$ is said to be {\it isometry-dual}. In this paper, we first confirm a conjecture about the isometry-dual MDS elliptic codes…

Information Theory · Computer Science 2025-02-05 Yunlong Zhu , Chang-An Zhao

The main aim of this paper is to study $LCD$ codes. Linear code with complementary dual($LCD$) are those codes which have their intersection with their dual code as $\{0\}$. In this paper we will give rather alternative proof of Massey's…

Information Theory · Computer Science 2018-02-21 Nitin S. Darkunde , Arunkumar R. Patil

In this paper, we study the complementary dual codes in more general setting (which are called Galois LCD codes) by a uniform method. A necessary and sufficient condition for linear codes to be Galois LCD codes is determined, and…

Information Theory · Computer Science 2017-05-03 Xiusheng Liu , Yun Fan , Hualu Liu

Linear codes with complementary-duals (LCD) are linear codes that intersect with their dual trivially. Multinegacirculant codes of index $2$ that are LCD are characterized algebraically and some good codes are found in this family. Exact…

Information Theory · Computer Science 2017-03-10 Adel Alahmadi , Cem Güneri , Buket Özkaya , Hatoon Shoaib , Patrick Solé

Sum-rank codes are an important class of codes which can be utilized for linear network coding, space-time coding and distributed storage. They can not only reduce the size of network alphabet but also detect and correct more errors. Based…

Information Theory · Computer Science 2025-10-14 Qingfeng Xia , Hongwei Liu , Hao Chen , Xu Pan

Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…

Information Theory · Computer Science 2015-06-08 Steven T. Dougherty , Jon-Lark Kim , Buket Ozkaya , Lin Sok , Patrick Solé

Linear complementary dual (LCD) cyclic codes were referred historically to as reversible cyclic codes, which had applications in data storage. Due to a newly discovered application in cryptography, there has been renewed interest in LCD…

Information Theory · Computer Science 2017-09-12 Claude Carlet , Sihem Mesnager , Chunming Tang , Yanfeng Qi

In this paper, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction…

Information Theory · Computer Science 2017-04-14 Lin Sok , Minjia Shi , Patrick Solé

A subspace code is a nonempty set of subspaces of a vector space $\mathbb F^n_q$. Linear codes with complementary duals, or LCD codes, are linear codes whose intersection with their duals is trivial. In this paper, we introduce a notion of…

Combinatorics · Mathematics 2023-05-04 Dean Crnkovic , Andrea Svob

Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fields have been intensively studied recently due to their applications in cryptography, in the context of side-channel and fault injection…

Information Theory · Computer Science 2020-07-14 Cem Güneri , Edgar Martínez-Moro , Selcen Sayıcı

We establish a complete classification of binary group codes with complementary duals for a finite group and explicitly determine the number of linear complementary dual (LCD) cyclic group codes by using cyclotomic cosets. The dimension and…

Information Theory · Computer Science 2022-01-24 Ankan Shaw , Sanjit Bhowmick , Satya Bagchi

Linear codes with complementary duals (LCD) have a great deal of significance amongst linear codes. Maximum distance separable (MDS) codes are also an important class of linear codes since they achieve the greatest error correcting and…

Information Theory · Computer Science 2019-09-17 Mehmet E. Koroglu , Mustafa Sarı

Linear complementary dual (LCD) codes over finite fields are linear codes satisfying $C\cap C^{\perp}=\{0\}$. We generalize the LCD codes over finite fields to $\mathbb{Z}_2\mathbb{Z}_2[u]$-LCD codes over the ring…

Information Theory · Computer Science 2019-03-28 Hu Peng , Liu Xiusheng

We give two methods for constructing many linear complementary dual (LCD for short) codes from a given LCD code, by modifying some known methods for constructing self-dual codes. Using the methods, we construct binary LCD codes and…

Information Theory · Computer Science 2021-01-29 Masaaki Harada

Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary…

Information Theory · Computer Science 2020-03-18 Yansheng Wu , Yoonjin Lee

In this paper, we investigate the structure and properties of additive complementary dual (ACD) codes over the mixed alphabet $\mathbb{F}_2\mathbb{F}_4$ relative to a certain inner product defined over $\mathbb{F}_2\mathbb{F}_4$. We…

Information Theory · Computer Science 2025-08-08 S. Ouagagui , N. Benbelkacem , A. Batoul , T. Abualrub