English
Related papers

Related papers: Classification and count of binary linear compleme…

200 papers

In this paper, we investigate the rank-metric codes which are proposed by Delsarte and Gabidulin to be complementary dual codes. We point out the relationship between Delsarte complementary dual codes and Gabidulin complementary dual codes.…

Information Theory · Computer Science 2017-08-04 Xiusheng Liu , Hualu Liu

It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…

Quantum Physics · Physics 2007-05-23 Eric M. Rains

In this paper we construct infinite families of non-linear maximum rank distance codes by using the setting of bilinear forms of a finite vector space. We also give a geometric description of such codes by using the cyclic model for the…

Information Theory · Computer Science 2017-04-10 Nicola Durante , Alessandro Siciliano

Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…

Information Theory · Computer Science 2021-07-02 Nuh Aydin , R. Oliver VandenBerg

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

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

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

Both linear complementary dual (LCD) codes and maximum distance separable (MDS) codes have good algebraic structures, and they have interesting practical applications such as communication systems, data storage, quantum codes, and so on. So…

Information Theory · Computer Science 2021-05-19 Yansheng Wu , Jong Yoon Hyun , Yoonjin Lee

We classify 8-divisible binary linear codes with minimum distance 24 and small length. As an application we consider the codes associated to nodal sextics with 65 ordinary double points.

Information Theory · Computer Science 2020-12-14 Sascha Kurz

We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of We study (Galois) linear complementary dual codes over mixed alphabets arising…

Information Theory · Computer Science 2024-11-28 Maryam Bajalan , Alexandre Fotue-Tabue , Joël Kabore , Edgar Martínez-Moro

We introduce {\bf complementary information set codes} of higher-order. A binary linear code of length $tk$ and dimension $k$ is called a complementary information set code of order $t$ ($t$-CIS code for short) if it has $t$ pairwise…

Information Theory · Computer Science 2014-06-19 Claude Carlet , Finley Freibert , Sylvain Guilley , Michael Kiermaier , Jon-Lark Kim , Patrick Solé

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

Linear complementary dual codes (LCD codes) are codes whose intersections with their dual codes are trivial. These codes were introduced by Massey in 1992. LCD codes have wide applications in data storage, communication systems, and…

Information Theory · Computer Science 2023-02-07 Welington Santos

In this paper, we study the complementary dual codes in more general setting (which are called Galois LCD codes) by a uniform method. A necessary and sufficient condition for linear codes to be Galois LCD codes is determined, and…

Information Theory · Computer Science 2017-05-03 Xiusheng Liu , Yun Fan , Hualu Liu

In addition to their applications in data storage, communications systems, and consumer electronics, LCD codes -- a class of linear codes -- have been employed in cryptography recently. LCD cyclic codes were referred to as reversible cyclic…

Information Theory · Computer Science 2017-01-03 Chengju Li , Cunsheng Ding , Shuxing Li

Orbits of graphs under the operation edge local complementation (ELC) are defined. We show that the ELC orbit of a bipartite graph corresponds to the equivalence class of a binary linear code. The information sets and the minimum distance…

Combinatorics · Mathematics 2009-08-24 Lars Eirik Danielsen , Matthew G. Parker

Finite semisimple group algebras for which all the minimal ideals are easily computable dimension (ECD) are characterized and some lower bounds for the minimum Hamming distance of group codes in these algebras are offered. Examples…

Representation Theory · Mathematics 2024-08-08 E. J. García-Claro

Binary cyclic codes having large dimensions and minimum distances close to the square-root bound are highly valuable in applications where high-rate transmission and robust error correction are both essential. They provide an optimal…

Information Theory · Computer Science 2025-04-22 Mrinal Kanti Bose , Udaya Parampalli , Abhay Kumar Singh

A linear code is linear complementary dual (LCD) if it meets its dual trivially. LCD codes have been a hot topic recently due to Boolean masking application in the security of embarked electronics (Carlet and Guilley, 2014). Additive codes…

Information Theory · Computer Science 2022-07-06 Minjia Shi , Na Liu , Jon-Lark Kim , Patrick Solé

Self-orthogonal codes are a subclass of linear codes that are contained within their dual codes. Since self-orthogonal codes are widely used in quantum codes, lattice theory and linear complementary dual (LCD) codes, they have received…

Information Theory · Computer Science 2024-11-12 Yaozong Zhang , Dabin Zheng , Xiaoqiang Wang