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LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented to transform any linear code into an LCD code with the same parameters when it is supported on a finite field with cardinality…

Information Theory · Computer Science 2019-11-25 Carlos Galindo , Olav Geil , Fernando Hernando , Diego Ruano

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

Both maximum distance separable (MDS) codes that are not equivalent to generalized Reed-Solomon (GRS) codes (non-GRS MDS codes) and near MDS (NMDS) codes have nice applications in communication and storage systems. In this paper, we…

Information Theory · Computer Science 2025-01-28 Yang Li , Zhonghua Sun , Shixin Zhu

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

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

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

We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes, which greatly extends the class of…

Algebraic Geometry · Mathematics 2025-01-17 Fernando Hernando , Gary McGuire , Francisco Monserrat , Julio José Moyano-Fernández

Linear codes are the most important family of codes in cryptography and coding theory. Some codes have only a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs.…

Information Theory · Computer Science 2024-05-20 Shudi Yang , Tonghui Zhang , Zheng-An Yao

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

Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…

Information Theory · Computer Science 2024-01-08 Ziling Heng , Xiaoru Li , Yansheng Wu , Qi Wang

Kim et al. (2021) gave a method to embed a given binary $[n,k]$ code $\mathcal{C}$ $(k = 3, 4)$ into a self-orthogonal code of the shortest length which has the same dimension $k$ and minimum distance $d' \ge d(\mathcal{C})$. We extend this…

Information Theory · Computer Science 2022-06-28 Jon-Lark Kim , Whan-Hyuk Choi

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

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 the realm of algebraic geometric (AG) codes, characterizing dual codes has long been a challenging task. In this paper we introduces a generalized criterion to characterize self-orthogonality of AG codes based on residues, drawing upon…

Information Theory · Computer Science 2025-06-03 Puyin Wang , Jinquan Luo

In this paper, a criterion of MDS Euclidean self-orthogonal codes is presented. New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square $q$,…

Information Theory · Computer Science 2019-10-01 Xiaolei Fang , Meiqing Liu , Jinquan Luo

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

Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed…

Information Theory · Computer Science 2015-10-20 Zhengchun Zhou , Nian Li , Cuiling Fan , Tor Helleseth

Low-density parity check (LDPC) codes are a significant class of classical codes with many applications. Several good LDPC codes have been constructed using random, algebraic, and finite geometries approaches, with containing cycles of…

Quantum Physics · Physics 2016-11-18 Salah A. Aly

Linear codes with few weights have many applications in secret sharing schemes, authentication codes, communication and strongly regular graphs. In this paper, we consider linear codes with three weights in arbitrary characteristic. To do…

Information Theory · Computer Science 2017-03-27 Sihem Mesnager , Ferruh Özbudak , Ahmet Sınak

In this paper, several classes of three-weight ternary linear codes from non-weakly regular dual-bent functions are constructed based on a generic construction method. Instead of the whole space, we use the subspaces $B_+(f)$ or $B_-(f)$…

Information Theory · Computer Science 2022-01-19 Rumi Melih Pelen