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In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring $R=\F_{q}+v\F_{q}+v^{2}\F_{q}$, where $v^{3}=v$, for $q$ odd. We give conditions on the existence of LCD codes and…

Information Theory · Computer Science 2017-04-13 A. Melakhessou , K. Guenda , T. A. Gulliver , M. Shi , P. Solé

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

Linear complementary dual (LCD) codes are linear codes that intersect with their dual codes trivially. We study the largest minimum weight $d_2(n,k)$ among all binary LCD $[n,k]$ codes and the largest minimum weight $d_3(n,k)$ among all…

Information Theory · Computer Science 2020-11-19 Makoto Araya , Masaaki Harada , Ken Saito

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 codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual are trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault…

Information Theory · Computer Science 2017-03-17 Claude Carlet , Sihem Mesnager , Chunming Tang , Yanfeng Qi

Locally recoverable (LRC) codes provide a solution to single node failure in distributed storage systems, where it is a very common problem. On the other hand, linear complementary dual (LCD) codes are useful in fault injections attacks on…

Information Theory · Computer Science 2020-11-09 Charul Rajput , Maheshanand Bhaintwal , Ramakrishna Bandi

In this paper, we show that LCD codes are not equivalent to linear codes over small finite fields. The enumeration of binary optimal LCD codes is obtained. We also get the exact value of LD$(n,2)$ over $\mathbb{F}_3$ and $\mathbb{F}_4$. We…

Information Theory · Computer Science 2021-01-22 Binbin Pang , Shixin Zhu , Xiaoshan Kai

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

Recently, Linear Complementary Dual (LCD) codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes. This paper directs its attention to the construction of binary and…

Information Theory · Computer Science 2024-09-13 Yansheng Wu , Jin Ma , Shandong Yang

In the recent years, there has been active research on self-orthogonal embeddings of linear codes since they yielded some optimal self-orthogonal codes. LCD codes have a trivial hull so they are counterparts of self-orthogonal codes. So it…

Information Theory · Computer Science 2026-01-29 Junmin An , Ji-Hoon Hong , Jon-Lark Kim , Haeun Lim

We give a complete characterization of simple graphs whose adjacency matrices generate binary linear complementary dual (LCD) codes. In particular, we completely characterize a distance-regular graph which yields an LCD code in terms of the…

Combinatorics · Mathematics 2026-05-18 Keita Ishizuka

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

A binary linear code is called {\em LCD} if it intersects its dual trivially. We show that the coefficients of the joint weight enumerator of such a code with its dual satisfy linear constraints, leading to a new linear programming bound on…

Metric Geometry · Mathematics 2015-12-01 Adel Alahmadi , Michel Deza , Mathieu Dutour Sikirić , Patrick Solé

A linear code is said to be self-orthogonal if it is contained in its dual. Self-orthogonal codes are of interest because of their important applications, such as for constructing linear complementary dual (LCD) codes and quantum codes. In…

Information Theory · Computer Science 2023-12-08 Dengcheng Xie , Shixin Zhu , Yang Li

From a given $[n, k]$ code $C$, we give a method for constructing many $[n, k]$ codes $C'$ such that the hull dimensions of $C$ and $C'$ are identical. This method can be applied to constructions of both self-dual codes and linear…

Information Theory · Computer Science 2021-08-31 Keita Ishizuka , Ken Saito

In this work, we propose two criteria for linear codes obtained from the Plotkin sum construction being symplectic self-orthogonal (SO) and linear complementary dual (LCD). As specific constructions, several classes of symplectic SO codes…

Information Theory · Computer Science 2023-11-01 Shixin Zhu , Yang Li , Shitao Li

Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual is trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault…

Information Theory · Computer Science 2017-03-14 Claude Carlet , Sihem Mesnager , Chunming Tang , Yanfeng Qi

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 (LCD) codes introduced by Massey are the codes whose intersections with their dual codes are trivial. It can help to improve the security of the information processed by sensitive devices, especially against…

Information Theory · Computer Science 2020-12-29 Liangdong Lu , Ruihu Li , Qiang Fu , Chen Xuan , Wenping Ma

In the 2017 paper by Dougherty, Kim, Ozkaya, Sok, and Sol\'e about the linear programming bound for LCD codes the notion $\mathrm{LCD}[n,k]$ was defined for binary LCD $[n,k]$-codes. We find the formula for $\mathrm{LCD}[n,2]$.

Commutative Algebra · Mathematics 2019-09-04 Seth Gannon , Hamid Kulosman