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Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian…

信息论 · 计算机科学 2014-03-12 Bocong Chen , San Ling , Guanghui Zhang

In this paper, two classes of quantum MDS codes are constructed. The main tools are multiplicative structures on finite fields. Carefully choosing different cosets can make the corresponding generalized Reed-Solomon codes Hermitian…

信息论 · 计算机科学 2024-10-24 Puyin Wang , Jinquan Luo

We generalized to higher dimensions the notions of optical orthogonal codes. We establish uper bounds on the capacity of general $ n $-dimensional OOCs, and on specific types of ideal codes (codes with zero off-peak autocorrelation). The…

组合数学 · 数学 2022-07-18 Tim Alderson

Near MDS (NMDS) codes are closely related to interesting objects in finite geometry and have nice applications in combinatorics and cryptography. But there are many unsolved problems about construction of NMDS codes. In this paper, by using…

信息论 · 计算机科学 2024-06-17 Shanqi Pang , Chaomeng Zhang , Mengqian Chen , Miaomiao Zhang

A simple construction of quaternary hermitian self-orthogonal codes with parameters $[2n+1,k+1]$ and $[2n+2,k+2]$ from a given pair of self-orthogonal $[n,k]$ codes, and its link to quantum codes is considered. As an application, an optimal…

信息论 · 计算机科学 2013-12-10 Vladimir D. Tonchev

In this paper, a criterion of MDS Euclidean self-orthogonal codes is presented. New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square $q$,…

信息论 · 计算机科学 2019-10-01 Xiaolei Fang , Meiqing Liu , Jinquan Luo

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.…

信息论 · 计算机科学 2017-10-16 Somphong Jitman , Todsapol Mankean

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…

信息论 · 计算机科学 2023-11-01 Shixin Zhu , Yang Li , Shitao Li

There has been a lot of effort to construct good quantum codes from the classical error correcting codes. Constructing new quantum codes, using Hermitian self-orthogonal codes, seems to be a difficult problem in general. In this paper,…

信息论 · 计算机科学 2021-12-14 Lin Sok

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…

信息论 · 计算机科学 2017-04-14 Lin Sok , Minjia Shi , Patrick Solé

Quantum maximum-distance-separable (MDS for short) codes are an important class of quantum codes. In this paper, by using Hermitian self-orthogonal generalized Reed-Solomon (GRS for short) codes, we construct five new classes of $q$-ary…

信息论 · 计算机科学 2023-07-11 Ruhao Wan , Shixin Zhu

In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS…

信息论 · 计算机科学 2016-10-26 Minjia Shi , Lin Sok , Patrick Solé

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…

组合数学 · 数学 2026-02-24 Xiuling Shan , Lidong Wang , Yanxun Chang , Xiaomiao Wang

In this paper, we mainly use classical Hermitian self-orthogonal generalized Reed-Solomon codes to construct two new classes of quantum MDS codes. Most of our quantum MDS codes have minimum distance larger than q/2+1. Compared with…

信息论 · 计算机科学 2020-03-24 Weiwei Wang , Jiantao Li

The construction of quantum error-correcting codes (QECCs) with good parameters is a hot topic in the area of quantum information and quantum computing. Quantum maximum distance separable (QMDS) codes are optimal because the minimum…

量子物理 · 物理学 2024-06-18 Shanqi Pang , Mengqian Chen , Rong Yan , Yan Zhu

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…

组合数学 · 数学 2019-12-02 Dean Crnkovic , Ronan Egan , B. G. Rodrigues , Andrea Svob

Quasi-cyclic codes have been recently employed in the constructions of quantum error-correcting codes. In this paper, we propose a construction of infinite families of quasi-cyclic codes over $\F_q$ which are self-orthogonal with respect to…

信息论 · 计算机科学 2026-05-25 Gustavo Terra Bastos , Angelynn Álvarez , Cameron Williams

Self-dual codes have been studied actively because they are connected with mathematical structures including block designs and lattices and have practical applications in quantum error-correcting codes and secret sharing schemes.…

密码学与安全 · 计算机科学 2024-09-04 Minjia Shi , Sihui Tao , Jihoon Hong , Jon-Lark Kim

In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss…

代数几何 · 数学 2019-12-18 Daniele Bartoli , Maria Montanucci , Giovanni Zini

Recently, Yaakobi et al. introduced codes for $b$-symbol read channels, where the read operation is performed as a consecutive sequence of $b>2$ symbols. In this paper, we establish a Singleton-type bound on $b$-symbol codes. Codes meeting…

信息论 · 计算机科学 2016-09-30 Baokun Ding , Tao Zhang , Gennian Ge