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Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study the largest minimum weight $d(n,k)$ among all binary linear complementary dual $[n,k]$ codes. We…

Combinatorics · Mathematics 2020-11-20 Makoto Araya , Masaaki Harada

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

Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. These codes were first introduced by Massey in 1964. Nowadays, LCD codes are extensively studied in the…

Information Theory · Computer Science 2021-09-15 Stefka Bouyuklieva

Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual $[n,k]$ codes with the largest minimum weight among all binary…

Combinatorics · Mathematics 2020-11-20 Masaaki Harada , Ken Saito

Linear complementary dual (LCD) codes can be used to against side-channel attacks and fault noninvasive attacks. Let $d_{a}(n,6)$ and $d_{l}(n,6)$ be the minimum weights of all binary optimal linear codes and LCD codes with length $n$ and…

Information Theory · Computer Science 2024-09-26 Yang Liu , Ruihu Li

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

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

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

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

Hermitian linear complementary dual codes are linear codes whose intersection with their Hermitian dual code is trivial. The largest minimum weight among quaternary Hermitian linear complementary dual codes of dimension $2$ is known for…

Combinatorics · Mathematics 2020-04-21 Keita Ishizuka

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

We show that any ternary Euclidean (resp.\ quaternary Hermitian) linear complementary dual $[n,k]$ code contains a Euclidean (resp.\ Hermitian) linear complementary dual $[n,k-1]$ subcode for $2 \le k \le n$. As a consequence, we derive a…

Information Theory · Computer Science 2020-11-20 Masaaki Harada , Ken Saito

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

Let $t \in \{2,8,10,12,14,16,18\}$ and $n=31s+t\geq 14$, $d_{a}(n,5)$ and $d_{l}(n,5)$ be distances of binary $[n,5]$ optimal linear codes and optimal linear complementary dual (LCD) codes, respectively. We show that an $[n,5,d_{a}(n,5)]$…

Information Theory · Computer Science 2024-09-26 Yang Liu , Ruihu Li , Qiang Fu , Hao Song

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

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 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

The hull of a linear code over finite fields is the intersection of the code and its dual, and linear codes with small hulls have applications in computational complexity and information protection. Linear codes with the smallest hull are…

Information Theory · Computer Science 2023-06-08 Shitao Li , Minjia Shi , Jon-Lark Kim

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

The largest minimum weights among quaternary Hermitian linear complementary dual codes are known for dimension $2$. In this paper, we give some conditions for the nonexistence of quaternary Hermitian linear complementary dual codes with…

Combinatorics · Mathematics 2020-11-20 Makoto Araya , Masaaki Harada , Ken Saito
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