English
Related papers

Related papers: On Z2Z4-additive complementary dual codes and rela…

200 papers

We study additive quaternary codes whose parameters are close to those of the extended cyclic [12; 6; 6]4-code or to the quaternary linear codes generated by the elliptic quadric in PG(3; 4) or its dual. In particular we characterize those…

Combinatorics · Mathematics 2018-04-10 Juergen Bierbrauer , Stefano Marcugini , Fernanda Pambianco

In this work, we investigate additive complementary dual (ACD) codes and their construction over finite fields $\mathbb{F}_{q^2}$ with respect to the trace inner products, where $q$ is a prime power. First, we associate an additive code…

Information Theory · Computer Science 2025-10-21 Gyanendra K. Verma , R. K. Sharma

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

The $\mathbb{Z}_{2^s}$-additive codes are subgroups of $\mathbb{Z}^n_{2^s}$, and can be seen as a generalization of linear codes over $\mathbb{Z}_2$ and $\mathbb{Z}_4$. A $\mathbb{Z}_{2^s}$-linear Hadamard code is a binary Hadamard code…

Information Theory · Computer Science 2018-01-17 Cristina Fernández-Córdoba , Carlos Vela , Mercè Villanueva

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

Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fields have been intensively studied recently due to their applications in cryptography, in the context of side-channel and fault injection…

Information Theory · Computer Science 2020-07-14 Cem Güneri , Edgar Martínez-Moro , Selcen Sayıcı

In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…

Information Theory · Computer Science 2022-01-03 Yansheng Wu , Chengju Li , Fu Xiao

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

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

We consider (symmetric, non-degenerate) bilinear spaces over a finite field and investigate the properties of their $\ell$-complementary subspaces, i.e., the subspaces that intersect their dual in dimension $\ell$. This concept generalizes…

Information Theory · Computer Science 2022-12-16 Heide Gluesing-Luerssen , Alberto Ravagnani

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) 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

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

An additive code is an $\mathbb{F}_q$-linear subspace of $\mathbb{F}_{q^m}^n$ over $\mathbb{F}_{q^m}$, which is not a linear subspace over $\mathbb{F}_{q^m}$. Linear complementary pairs (LCP) of codes have important roles in cryptography,…

Information Theory · Computer Science 2024-09-26 Sanjit Bhowmick , Deepak Kumar Dalai

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

We call a linear code $C$ with length $n$ over a field $F$, a linear complementary equi-dual code, when there exists a linear code $D$ over $F$ such that $D$ is permutation equivalent to $C^\perp$ and $(C,D)$ is a linear complementary pair…

Information Theory · Computer Science 2024-08-13 Ashkan Nikseresht , Shohreh Namazi , Marziyeh Beygi Khormaei

Since Massey introduced linear complementary dual (LCD) codes in 1992 and Bhasin et al. later formalized linear complementary pairs (LCPs) of codes - structures with important cryptographic applications - these code families have attracted…

Algebraic Geometry · Mathematics 2025-06-02 Adler Marques , Luciane Quoos

The applications of additive codes mainly lie in quantum error correction and quantum computing. Due to their applications in quantum codes, additive codes have grown in importance. In addition to this, additive codes allow the…

Information Theory · Computer Science 2024-01-03 Astha Agrawal , R. K. Sharma

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

This paper investigates the algebraic structure of additive complementary pairs of cyclic codes over a finite commutative ring. We demonstrate that for every additive complementary pair of additive cyclic codes, both constituent codes are…

Information Theory · Computer Science 2025-06-13 Sanjit Bhowmick , Kuntal Deka , Alexandre Fotue Tabue , Edgar Martínez-Moro