English
Related papers

Related papers: Construction of quaternary Hermitian LCD codes

200 papers

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

We propose a method for a classification of quaternary Hermitian LCD codes having large minimum weights. As an example, we give a classification of quaternary optimal Hermitian LCD codes of dimension 3.

Information Theory · Computer Science 2021-09-24 Makoto Araya , Masaaki Harada

We introduce quaternary modified four $\mu$-circulant codes as a modification of four circulant codes. We give basic properties of quaternary modified four $\mu$-circulant Hermitian self-dual codes. We also construct quaternary modified…

Information Theory · Computer Science 2024-01-30 Masaaki Harada

In this article, first we present a method for constructing many Hermitian LCD codes from a given Hermitian LCD code, and then provide several methods which utilize either a given [n, k, d] linear code or a given [n, k, d] Galois LCD code…

Information Theory · Computer Science 2023-10-09 Gyanendra K. Verma , Astha Agrawal , R. K. Sharma

Linear complementary dual (LCD) codes, which is a class of linear codes introduced by Massey, have been extensively studied in literature recently. It has been shown that LCD codes can help to improve the security of the information…

Information Theory · Computer Science 2020-10-21 Liangdong Lu , Xiuzhen Zhan , Sen Yang , Hao Cao

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 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

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

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 paper, we give a method for constructing linear codes with small hulls by generalizing the method in \cite{LCD-T-matric}. As a result, we obtain many optimal Euclidean LCD codes and Hermitian LCD codes, which improve the previously…

Information Theory · Computer Science 2022-04-12 Shitao Li

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 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

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

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. It was proved that asymptotically good Hermitian LCD codes exist.…

Information Theory · Computer Science 2017-01-17 Chengju Li

This paper introduces a class of Hermitian LCD $2$-quasi-abelian codes over finite fields and presents a comprehensive enumeration of these codes in which relative minimum weights are small. We show that such codes are asymptotically good…

Information Theory · Computer Science 2026-01-08 Sanjit Bhowmick , Kuntal Deka

We establish the existence of optimal maximal entanglement entanglement-assisted quantum $[[n,k,d;n-k]]_2$ codes for $(n,k,d)=(14,6,7)$, $(15,7,7)$, $(17,6,9)$, $(17,7,8)$, $(19,7,9)$ and $(20,7,10)$. These codes are obtained from…

Combinatorics · Mathematics 2020-11-20 Masaaki Harada

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

Linear codes with small hulls over finite fields have been extensively studied due to their practical applications in computational complexity and information protection. In this paper, we develop a general method to determine the exact…

Information Theory · Computer Science 2022-11-29 Shitao Li , Minjia Shi , Huizhou 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

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
‹ Prev 1 2 3 10 Next ›