English
Related papers

Related papers: Matrix-Product Complementary dual Codes

200 papers

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

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

A linear code with a complementary dual (or LCD code) is defined to be a linear code $C$ whose dual code $C^{\perp}$ satisfies $C \cap C^{\perp}$= $\left\{ \mathbf{0}\right\} $. Let $LCD{[}n,k{]}$ denote the maximum of possible values of…

Information Theory · Computer Science 2017-01-17 Lucky Galvez , Jon-Lark Kim , Nari Lee , Young Gun Roe , Byung-Sun Won

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

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

A linear code is linear complementary dual (LCD) if it meets its dual trivially. LCD codes have been a hot topic recently due to Boolean masking application in the security of embarked electronics (Carlet and Guilley, 2014). Additive codes…

Information Theory · Computer Science 2022-07-06 Minjia Shi , Na Liu , Jon-Lark Kim , Patrick Solé

Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information…

Information Theory · Computer Science 2023-02-14 Shitao Li , Minjia Shi , Huizhou Liu

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 linear code $C$ with the property that $C \cap C^{\perp} = \{0 \}$ is said to be a linear complementary dual, or LCD, code. In this paper, we consider generalized affine Cartesian codes which are LCD. Generalized affine Cartesian codes…

Information Theory · Computer Science 2024-02-07 Hiram H. López , Felice Manganiello , Gretchen L. Matthews

Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over $\mathbb{F}_q$ having large minimum weights for $q \in \{2,3\}$. Using the characterization, we…

Combinatorics · Mathematics 2021-01-05 Makoto Araya , Masaaki Harada , Ken Saito

In recent years, linear complementary pairs (LCP) of codes and linear complementary dual (LCD) codes have gained significant attention due to their applications in coding theory and cryptography. In this work, we construct explicit LCPs of…

Algebraic Geometry · Mathematics 2024-12-31 Alonso S. Castellanos , Adler V. Marques , Luciane Quoos

Linear complementary dual (LCD) maximum distance separable (MDS) codes are constructed to given specifications. For given $n$ and $r<n$, with $n$ or $r$ (or both) odd, MDS LCD $(n,r)$ codes are constructed over finite fields whose…

Information Theory · Computer Science 2020-05-19 Ted Hurley

We provide a polynomial approach to investigate linear complementary dual (LCD) quasi-cyclic codes over finite fields. We establish necessary and sufficient conditions for LCD quasi-cyclic codes of index 2 with respect to the Euclidean,…

Information Theory · Computer Science 2026-01-21 Kanat Abdukhalikov , Duy Ho , San Ling , Gyanendra K. Verma

Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This…

Information Theory · Computer Science 2017-02-28 Bocong Chen , Hongwei Liu

We call a linear code $C$ with length $n$ over a field $F$, a linear complementary equi-dual code, when there exists a linear code $D$ over $F$ such that $D$ is permutation equivalent to $C^\perp$ and $(C,D)$ is a linear complementary pair…

Information Theory · Computer Science 2024-08-13 Ashkan Nikseresht , Shohreh Namazi , Marziyeh Beygi Khormaei

Linear codes with complementary duals are linear codes whose intersection with their duals are trivial, shortly named LCD codes. In this paper we outline a construction for LCD codes over finite fields of order $q$ using weighing matrices…

Combinatorics · Mathematics 2019-12-02 Dean Crnkovic , Ronan Egan , B. G. Rodrigues , Andrea Svob

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

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

The Euclidean hull of a linear code $C$ is defined as $C\cap C^{\perp}$, where $C^\perp$ denotes the dual of $C$ under the Euclidean inner product. A linear code with zero hull dimension is called a linear complementary dual (LCD) code. A…

Information Theory · Computer Science 2023-04-25 Zohreh Aliabadi , Tekgül Kalaycı

Linear complementary pairs (LCP) of codes play an important role in armoring implementations against side-channel attacks and fault injection attacks. One of the most common ways to construct LCP of codes is to use Euclidean linear…

Information Theory · Computer Science 2017-07-28 Claude Carlet , Sihem Mesnager , Chunming Tang , Yanfeng Qi
‹ Prev 1 2 3 10 Next ›