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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 binary linear complementary dual $[n,k]$ codes with the largest minimum weight among all binary…

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

A complete classification of binary doubly even self-dual codes of length 40 is given. As a consequence, a classification of binary extremal self-dual codes of length 38 is also given.

Combinatorics · Mathematics 2012-11-13 Koichi Betsumiya , Masaaki Harada , Akihiro Munemasa

Ternary self-dual codes have been classified for lengths up to 20. At length 24, a classification of only extremal self-dual codes is known. In this paper, we give a complete classification of ternary self-dual codes of length 24 using the…

Combinatorics · Mathematics 2012-05-28 Masaaki Harada , Akihiro Munemasa

A complete classification of binary self-dual codes of length 36 is given.

Combinatorics · Mathematics 2012-11-13 Masaaki Harada , Akihiro Munemasa

An efficient algorithm for classification of binary self-dual codes is presented. As an application, a complete classification of the self-dual codes of length 38 is given.

Combinatorics · Mathematics 2012-10-10 Stefka Bouyuklieva , Iliya Bouyukliev

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

All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact…

Information Theory · Computer Science 2016-11-18 Iliya Bouyukliev , Erik Jakobsson

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

The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of…

Combinatorics · Mathematics 2016-11-18 Tsonka Baicheva , Iliya Bouyukliev , Stefan Dodunekov , Veerle Fack

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 (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 (LCD) are linear codes satisfying $C\cap C^{\perp}=\{0\}$. Under suitable conditions, matrix-product codes that are complementary dual codes are characterized. We construct LCD codes using quasi-orthogonal…

Information Theory · Computer Science 2016-04-14 Xiusheng Liu , Hualu Liu

Ternary maximal self-orthogonal codes have been classified for lengths up to $24$. In this note, we provide a complete classification of ternary maximal self-orthogonal codes of length $25$.

Information Theory · Computer Science 2026-05-14 Makoto Araya , Masaaki Harada

A classification of quaternary Hermitian self-dual codes of length 20 is given. Using this classification, a classification of extremal quaternary Hermitian self-dual codes of length 22 is also given.

Combinatorics · Mathematics 2012-05-28 Masaaki Harada , Akihiro Munemasa

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

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 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

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 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
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