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Both maximum distance separable (MDS) codes that are not equivalent to generalized Reed-Solomon (GRS) codes (non-GRS MDS codes) and near MDS (NMDS) codes have nice applications in communication and storage systems. In this paper, we…

Information Theory · Computer Science 2025-01-28 Yang Li , Zhonghua Sun , Shixin Zhu

Recently, the notions of self-orthogonal subspace codes and LCD subspace codes were introduced, and LCD subspace codes obtained from mutually unbiased weighing matrices were studied. In this paper, we provide a method of constructing…

Combinatorics · Mathematics 2024-07-09 Dean Crnković , Keita Ishizuka , Hadi Kharaghani , Sho Suda , Andrea Švob

Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary…

Information Theory · Computer Science 2016-12-15 Deng Tang , Claude Carlet , Zhengchun Zhou

In this work, our main objective is to construct quantum codes from quasi-twisted (QT) codes. At first, a necessary and sufficient condition for Hermitian self-orthogonality of QT codes is introduced by virtue of the Chinese Remainder…

Information Theory · Computer Science 2020-01-07 Jingjie Lv , Ruihu Li , Junli Wang

We give a method of constructing self-orthogonal codes from equitable partitions of association schemes. By applying this method we construct self-orthogonal codes from some distance-regular graphs. Some of the obtained codes are optimal.…

Combinatorics · Mathematics 2019-03-06 Dean Crnkovic , Sanja Rukavina , Andrea Svob

We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes, which greatly extends the class of…

Algebraic Geometry · Mathematics 2025-01-17 Fernando Hernando , Gary McGuire , Francisco Monserrat , Julio José Moyano-Fernández

Self-orthogonal codes have been of interest due to there rich algebraic structures and wide applications. Euclidean self-orthogonal codes have been quite well studied in literature. Here, we have focused on Hermitian self-orthogonal codes.…

Information Theory · Computer Science 2017-10-16 Somphong Jitman , Todsapol Mankean

In this paper, for an odd prime $p$, several classes of two-weight linear codes over the finite field $\mathbb{F}_p$ are constructed from the defining sets, and then their complete weight distributions are determined by employing character…

Information Theory · Computer Science 2021-11-22 Canze Zhu , Qunying Liao

We first establish a simple yet powerful necessary and sufficient condition for a binary linear code to be SO, leading to a complete characterization of singly-even codes in this family. We further derive necessary and sufficient conditions…

Information Theory · Computer Science 2026-01-07 Kangquan Li , Hao Chen , Wengang Jin , Longjiang Qu

A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the…

Information Theory · Computer Science 2015-03-24 Cunsheng Ding

Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…

Information Theory · Computer Science 2024-01-08 Ziling Heng , Xiaoru Li , Yansheng Wu , Qi Wang

In the realm of algebraic geometric (AG) codes, characterizing dual codes has long been a challenging task. In this paper we introduces a generalized criterion to characterize self-orthogonality of AG codes based on residues, drawing upon…

Information Theory · Computer Science 2025-06-03 Puyin Wang , Jinquan Luo

Let $\mathbb{F}_{p^m}$ be the finite field of order $p^m$, where $p$ is an odd prime and $m$ is a positive integer. In this paper, we investigate a class of subfield codes of linear codes and obtain the weight distribution of…

Information Theory · Computer Science 2019-10-15 Xiaoqiang Wang , Dabin Zheng , Yan Zhang

Projective two-weight linear codes are closely related to finite projective spaces and strongly regular graphs. In this paper, a family of $q$-ary projective two-weight linear codes is presented, where $q$ is a power of 2. The parameters of…

Information Theory · Computer Science 2021-03-26 Ziling Heng , Dexiang Li , Jiao Du , Fuling Chen

We complete the building-up construction for self-dual codes by resolving the open cases over $GF(q)$ with $q \equiv 3 \pmod 4$, and over $\Z_{p^m}$ and Galois rings $\GR(p^m,r)$ with an odd prime $p$ satisfying $p \equiv 3 \pmod 4$ with…

Information Theory · Computer Science 2012-01-30 Yoonjin Lee , Jon-Lark Kim

Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain…

Information Theory · Computer Science 2022-11-01 Meng Cao

A $q$-ary $t$-$(n,w,\lambda)$ design is a collection $\mathcal{A}$ of vectors of weight $w$ in $\mathbb{F}_{q}^{n}$ with the property that every vector of weight $t$ in $\mathbb{F}_{q}^{n}$ is contained in exactly $\lambda$ members of…

Information Theory · Computer Science 2026-03-16 Xinghao Wu , Junling Zhou

This paper introduces a new combinatorial construction for q-ary constant-weight codes which yields several families of optimal codes and asymptotically optimal codes. The construction reveals intimate connection between q-ary…

Information Theory · Computer Science 2007-07-13 Yeow Meng Chee , San Ling

A Type IV-II Z4-code is a self-dual code over Z4 with the property that all Euclidean weights are divisible by eight and all codewords have even Hamming weight. In this paper we use generalized bent functions for a construction of…

Information Theory · Computer Science 2022-11-03 Sara Ban , Sanja Rukavina

The study of optical orthogonal codes has been motivated by an application in an optical code-division multiple access system. This paper focuses on optimal two-dimensional optical orthogonal codes with autocorrelation and cross-correlation…

Combinatorics · Mathematics 2026-02-24 Xiuling Shan , Lidong Wang , Yanxun Chang , Xiaomiao Wang