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Linear complementary dual (LCD) maximum distance separable (MDS) codes are constructed to given specifications. For given $n$ and $r<n$, with $n$ or $r$ (or both) odd, MDS LCD $(n,r)$ codes are constructed over finite fields whose…

Information Theory · Computer Science 2020-05-19 Ted Hurley

A linear code $C$ with the property that $C \cap C^{\perp} = \{0 \}$ is said to be a linear complementary dual, or LCD, code. In this paper, we consider generalized affine Cartesian codes which are LCD. Generalized affine Cartesian codes…

Information Theory · Computer Science 2024-02-07 Hiram H. López , Felice Manganiello , Gretchen L. Matthews

A binary linear code is called {\em LCD} if it intersects its dual trivially. We show that the coefficients of the joint weight enumerator of such a code with its dual satisfy linear constraints, leading to a new linear programming bound on…

Metric Geometry · Mathematics 2015-12-01 Adel Alahmadi , Michel Deza , Mathieu Dutour Sikirić , Patrick Solé

Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual are trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault…

Information Theory · Computer Science 2017-03-17 Claude Carlet , Sihem Mesnager , Chunming Tang , Yanfeng Qi

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

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

In 1964, Massey introduced a class of codes with complementary duals which are called Linear Complimentary Dual (LCD for short) codes. He showed that LCD codes have applications in communication system, side-channel attack (SCA) and so on.…

Information Theory · Computer Science 2017-10-06 Peter Beelen , Lingfei Jin

Linear complementary pairs (LCP) of codes play an important role in armoring implementations against side-channel attacks and fault injection attacks. One of the most common ways to construct LCP of codes is to use Euclidean linear…

Information Theory · Computer Science 2017-07-28 Claude Carlet , Sihem Mesnager , Chunming Tang , Yanfeng Qi

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 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

Linear codes with complementary duals (LCD) have a great deal of significance amongst linear codes. Maximum distance separable (MDS) codes are also an important class of linear codes since they achieve the greatest error correcting and…

Information Theory · Computer Science 2019-09-17 Mehmet E. Koroglu , Mustafa Sarı

Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual is trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault…

Information Theory · Computer Science 2017-03-14 Claude Carlet , Sihem Mesnager , Chunming Tang , Yanfeng Qi

It was shown by Massey that linear complementary dual (LCD for short) codes are asymptotically good. In 2004, Sendrier proved that LCD codes meet the asymptotic Gilbert-Varshamov (GV for short) bound. Until now, the GV bound still remains…

Information Theory · Computer Science 2017-03-07 Lingfei Jin , Chaoping Xing

In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring $R=\F_{q}+v\F_{q}+v^{2}\F_{q}$, where $v^{3}=v$, for $q$ odd. We give conditions on the existence of LCD codes and…

Information Theory · Computer Science 2017-04-13 A. Melakhessou , K. Guenda , T. A. Gulliver , M. Shi , P. Solé

Double circulant codes of length $2n$ over the semilocal ring $R = \mathbb{F}_q + u\mathbb{F}_q,\, u^2=u,$ are studied when $q$ is an odd prime power, and $-1$ is a square in $\mathbb{F}_q.$ Double negacirculant codes of length $2n$ are…

Information Theory · Computer Science 2018-06-11 Minjia Shi , Hongwei Zhu , Liqin Qian , Lin Sok , Patrick Solé

Polycyclic codes offer a natural generalization of cyclic codes and provide a broader algebraic framework for constructing linear codes with good parameters. In this paper, we study binary polycyclic codes associated with powers of…

Information Theory · Computer Science 2026-05-13 Sujata Bansal , Pramod Kumar Kewat

Double Toeplitz (DT) codes are codes with a generator matrix of the form $(I,T)$ with $T$ a Toeplitz matrix, that is to say constant on the diagonals parallel to the main. When $T$ is tridiagonal and symmetric we determine its spectrum…

Information Theory · Computer Science 2021-03-09 Minjia Shi , Ferruh Özbudak , Li Xu , Patrick Solé

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

Linear complementary dual (LCD) codes is a class of linear codes introduced by Massey in 1964. LCD codes have been extensively studied in literature recently. In addition to their applications in data storage, communications systems, and…

Information Theory · Computer Science 2016-10-19 Sihem Mesnager , Chunming Tang , Yanfeng Qi

This paper explores extremal self-dual double circulant (DC) codes and linear complementary dual (LCD) codes of arbitrary length over the Galois field $\mathbb F_2$. We establish the sufficient and necessary conditions for DC codes and…

Information Theory · Computer Science 2025-02-21 Wenyu Han , Tongjiang Yan , Ming Yan