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We establish a complete classification of binary group codes with complementary duals for a finite group and explicitly determine the number of linear complementary dual (LCD) cyclic group codes by using cyclotomic cosets. The dimension and…

Information Theory · Computer Science 2022-01-24 Ankan Shaw , Sanjit Bhowmick , Satya Bagchi

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 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

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

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

In this work, we propose two criteria for linear codes obtained from the Plotkin sum construction being symplectic self-orthogonal (SO) and linear complementary dual (LCD). As specific constructions, several classes of symplectic SO codes…

Information Theory · Computer Science 2023-11-01 Shixin Zhu , Yang Li , Shitao Li

A linear code is said to be self-orthogonal if it is contained in its dual. Self-orthogonal codes are of interest because of their important applications, such as for constructing linear complementary dual (LCD) codes and quantum codes. In…

Information Theory · Computer Science 2023-12-08 Dengcheng Xie , Shixin Zhu , Yang Li

In this paper, we give a method for constructing linear codes with small hulls by generalizing the method in \cite{LCD-T-matric}. As a result, we obtain many optimal Euclidean LCD codes and Hermitian LCD codes, which improve the previously…

Information Theory · Computer Science 2022-04-12 Shitao Li

Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…

Information Theory · Computer Science 2024-12-03 Cunsheng Ding

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

In this article, first we present a method for constructing many Hermitian LCD codes from a given Hermitian LCD code, and then provide several methods which utilize either a given [n, k, d] linear code or a given [n, k, d] Galois LCD code…

Information Theory · Computer Science 2023-10-09 Gyanendra K. Verma , Astha Agrawal , R. K. Sharma

In this paper, we investigate the structure and properties of additive complementary dual (ACD) codes over the mixed alphabet $\mathbb{F}_2\mathbb{F}_4$ relative to a certain inner product defined over $\mathbb{F}_2\mathbb{F}_4$. We…

Information Theory · Computer Science 2025-08-08 S. Ouagagui , N. Benbelkacem , A. Batoul , T. Abualrub

We introduce two constructions of additive codes over finite fields. Both constructions start with a linear code over a field with $q$ elements and give additive codes over the field with $q^h$ elements whose minimum distance is…

Information Theory · Computer Science 2025-06-05 Simeon Ball , Tabriz Popatia

Self-orthogonal codes are of interest as they have important applications in quantum codes, lattices and many areas. In this paper, based on the weakly regular plateaued functions or plateaued Boolean functions, we construct a family of…

Information Theory · Computer Science 2024-11-08 Peng Wang , Ziling Heng

We construct MDS Euclidean and Hermitian self-dual codes over large finite fields of odd and even characteristics. Our codes arise from cyclic and negacyclic duadic codes.

Information Theory · Computer Science 2010-04-08 Kenza Guenda

In this paper, we construct four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including…

Information Theory · Computer Science 2021-08-24 Zhao Hu , Nian Li , Xiangyong Zeng , Lisha Wang , Xiaohu Tang

Sum-rank codes are an important class of codes which can be utilized for linear network coding, space-time coding and distributed storage. They can not only reduce the size of network alphabet but also detect and correct more errors. Based…

Information Theory · Computer Science 2025-10-14 Qingfeng Xia , Hongwei Liu , Hao Chen , Xu Pan

Two families of complementary codes over finite fields $\mathbb{F}_q$ are studied, where $q=r^2$ is square: i) Hermitian complementary dual linear codes, and ii) trace Hermitian complementary dual subfield linear codes. Necessary and…

Information Theory · Computer Science 2017-10-13 Kriangkrai Boonniyom , Somphong Jitman

Self-orthogonal codes have received great attention due to their important applications in quantum codes, LCD codes and lattices. Recently, several families of self-orthogonal codes containing the all-$1$ vector were constructed by…

Information Theory · Computer Science 2025-08-06 Yadi Wei , Jiaxin Wang , Fang-Wei Fu

We study finite-field extensions that preserve the same support as the parity-check matrices defining a given binary CSS code. Here, an LDPC-CSS code refers to a CSS code whose parity-check matrices are orthogonal in the sense that each…

Quantum Physics · Physics 2025-10-30 Kenta Kasai