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Linear codes have been an interesting subject of study for many years. Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, a class of three-weight linear codes over Fp…

Information Theory · Computer Science 2015-12-24 Qiuyan Wang , Fei Li , Dongdai Lin

A short introduction to quantum error correction is given, and it is shown that zero-dimensional quantum codes can be represented as self-dual additive codes over GF(4) and also as graphs. We show that graphs representing several such codes…

Quantum Physics · Physics 2008-01-09 Lars Eirik Danielsen

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

In this paper, we apply two-to-one functions over $\mathbb{F}_{2^n}$ in two generic constructions of binary linear codes. We consider two-to-one functions in two forms: (1) generalized quadratic functions; and (2) $\left(x^{2^t}+x\right)^e$…

Information Theory · Computer Science 2020-06-23 Kangquan Li , Chunlei Li , Tor Helleseth , Longjiang Qu

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

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

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

We consider codes over the two semi-local non-unital rings of order six, \[ H_{23} = \langle a,b \mid 2a=0, 3b = 0, a^2=a, b^2 = 0, ab = 0 = ba \rangle,\] and \[H_{32} = \langle a,b \mid 2a=0, 3b = 0, a^2=0, b^2 = b, ab = 0 = ba \rangle. \]…

Rings and Algebras · Mathematics 2025-08-25 Altaf Alshuhail

We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal cyclic or duadic codes over F_4. An infinite family of…

Information Theory · Computer Science 2022-11-03 Reza Dastbasteh , Petr Lisonek

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

Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information…

Information Theory · Computer Science 2023-02-14 Shitao Li , Minjia Shi , Huizhou Liu

In this paper, we first generalize the class of linear codes by Ding and Ding (IEEE TIT, 61(11), pp. 5835-5842, 2015). Then we mainly study the augmented codes of this generalized class of linear codes. For one thing, we use Gaussian sums…

Information Theory · Computer Science 2024-04-30 Ziling Heng , Keqing Cao

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

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

Linear codes with few weights have significant applications in secret sharing schemes, authentication codes, association schemes, and strongly regular graphs. There are a number of methods to construct linear codes, one of which is based on…

Information Theory · Computer Science 2023-11-01 Yadi Wei , Jiaxin Wang , Fang-Wei Fu

Linear codes over finite fields parameterized by functions have proven to be a powerful tool in coding theory, yielding optimal and few-weight codes with significant applications in secret sharing, authentication codes, and association…

Information Theory · Computer Science 2026-02-17 Virginio Fratianni , Sihem Mesnager

In this paper we generalize the construction of binary self-orthogonal codes obtained from weakly self-orthogonal designs described by Tonchev in [12] in order to obtain self-orthogonal codes over an arbitrary field. We extend construction…

Combinatorics · Mathematics 2021-09-21 Vedrana Mikulić Crnković , Ivona Traunkar

In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which…

Quantum Physics · Physics 2009-11-13 Dan Hu , Weidong Tang , Meisheng Zhao , Qing Chen , Sixia Yu , C. H. Oh

Recently, simplicial complexes are used in constructions of several infinite families of minimal and optimal linear codes by Hyun {\em et al.} Building upon their research, in this paper more linear codes over the ring $\mathbb{Z}_4$ are…

Information Theory · Computer Science 2024-01-24 Yansheng Wu , Chao Li , Lin Zhang , Fu Xiao

Binary optimal codes often contain optimal or near-optimal subcodes. In this paper we show that this is true for the family of self-dual codes. One approach is to compute the optimum distance profiles (ODPs) of linear codes, which was…

Information Theory · Computer Science 2012-10-23 Finley Freibert , Jon-Lark Kim