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Related papers: New Constructions of Optimal Binary LCD Codes

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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 establish a connection between linear complementary dual (LCD) codes and caps in projective space. Using this framework and the structure theory of maximal caps, we derive nonexistence theorems for LCD codes with minimum distance at…

Information Theory · Computer Science 2026-04-07 Keita Ishizuka , Yuhi Kamio

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

A binary code of blocklength $n$ and codebook size $M$ is called an $(n,M)$ code, which is studied for memoryless binary symmetric channels (BSCs) with the maximum likelihood (ML) decoding. For any $n \geq 2$, some optimal codes among the…

Information Theory · Computer Science 2023-07-06 Yanyan Dong , Shenghao Yang

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

Linear complementary dual (LCD) cyclic codes were referred historically to as reversible cyclic codes, which had applications in data storage. Due to a newly discovered application in cryptography, there has been renewed interest in LCD…

Information Theory · Computer Science 2017-09-12 Claude Carlet , Sihem Mesnager , Chunming Tang , Yanfeng Qi

Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary…

Information Theory · Computer Science 2020-03-18 Yansheng Wu , Yoonjin Lee

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 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

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

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

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 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

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

In this paper, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction…

Information Theory · Computer Science 2017-04-14 Lin Sok , Minjia Shi , Patrick Solé

An additive quaternary $[n,k,d]$-code (length $n,$ quaternary dimension $k,$ minimum distance $d$) is a $2k$-dimensional F_2-vector space of $n$-tuples with entries in $Z_2\times Z_2$ (the $2$-dimensional vector space over F_2) with minimum…

Combinatorics · Mathematics 2020-07-13 Juergen Bierbrauer , Stefano Marcugini , Fernanda Pambianco

We consider the problem of finding $A_2(n,\{d_1,d_2\})$ defined as the maximal size of a binary (non-linear) code of length $n$ with two distances $d_1$ and $d_2$. Binary codes with distances $d$ and $d+2$ of size…

Combinatorics · Mathematics 2024-02-22 Ivan Landjev , Konstantin Vorob'ev

The hull of a linear code $C$ is the intersection of $C$ with its dual. To the best of our knowledge, there are very few constructions of binary linear codes with the hull dimension $\ge 2$ except for self-orthogonal codes. We propose a…

Information Theory · Computer Science 2023-06-13 Jon-Lark Kim

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

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