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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…

Combinatorics · Mathematics 2022-07-18 Tim Alderson

Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of…

Information Theory · Computer Science 2024-01-05 Somphong Jitman

The purpose of this paper is to present the structure of the linear codes over a finite field with q elements that have a permutation automorphism of order m. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic…

Information Theory · Computer Science 2024-02-05 Stefka Bouyuklieva

In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing…

Information Theory · Computer Science 2025-01-29 Puyin Wang , Jinquan Luo

Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…

Information Theory · Computer Science 2012-07-12 Cunsheng Ding

It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…

Information Theory · Computer Science 2023-01-09 Chaofeng Guan , Ruihu Li , Liangdong Lu , Yu Yao

MDS self-dual codes over finite fields have attracted a lot of attention in recent years by their theoretical interests in coding theory and applications in cryptography and combinatorics. In this paper we present a series of MDS self-dual…

Information Theory · Computer Science 2019-11-14 Aixian Zhang , Keqin Feng

Cyclic orbit codes are constant dimension subspace codes that arise as the orbit of a cyclic subgroup of the general linear group acting on subspaces in the given ambient space. With the aid of the largest subfield over which the given…

Information Theory · Computer Science 2014-03-06 Heide Gluesing-Luerssen , Katherine Morrison , Carolyn Troha

We propose a full-rate iterated space-time code construction, to design 2n-dimensional codes from n-dimensional cyclic algebra based codes. We give a condition to determine whether the resulting codes satisfy the full-diversity property,…

Information Theory · Computer Science 2013-03-12 Nadya Markin , Frederique Oggier

In this paper we characterize the orbit codes as geometrically uniform codes. This characterization is based on the description of all isometries over a projective geometry. In addition, the Abelian orbit codes are defined and a new…

Information Theory · Computer Science 2018-10-19 Gustavo Terra Bastos , Reginaldo Palazzo Júnior , Marinês Guerreiro

Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…

Information Theory · Computer Science 2015-06-08 Steven T. Dougherty , Jon-Lark Kim , Buket Ozkaya , Lin Sok , Patrick Solé

A circulant-based spatially-coupled (SC) code is constructed by partitioning the circulants in the parity-check matrix of a block code into several components and piecing copies of these components in a diagonal structure. By connecting…

Information Theory · Computer Science 2019-08-08 Homa Esfahanizadeh , Lev Tauz , Lara Dolecek

We improve on the lower bound of the maximum number of planes of ${\rm PG}(8,q)$ mutually intersecting in at most one point leading to the following lower bound: ${\cal A}_q(9, 4; 3) \ge q^{12}+2q^8+2q^7+q^6+q^5+q^4+1$ for constant…

Combinatorics · Mathematics 2019-05-28 Antonio Cossidente , Giuseppe Marino , Francesco Pavese

A novel code construction algorithm is presented to find all the possible code families for code reconfiguration in an OCDMA system. The algorithm is developed through searching all the complete subgraphs of a constructed graph. The…

Information Theory · Computer Science 2007-07-13 Xiang Lu , Jiajia Chen , Sailing He

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

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

A characterization of a class of optimal three-weight cyclic codes of dimension 3 over any finite field was recently presented in [10]. Shortly after this, a generalization for the sufficient numerical conditions of such characterization…

Information Theory · Computer Science 2016-09-26 Gerardo Vega

A lot of attention has been paid to the investigation of the algebraic properties of linear codes. In most cases, this investigation involves the determination of required code automorphisms, which are useful for decoders, such as the…

Combinatorics · Mathematics 2024-06-04 Ma Jicheng , Yan Guiying

Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary…

Information Theory · Computer Science 2020-03-18 Yansheng Wu , Yoonjin Lee

A subspace of a finite field is called a Sidon space if the product of any two of its nonzero elements is unique up to a scalar multiplier from the base field. Sidon spaces, introduced by Roth et al. (IEEE Trans Inf Theory 64(6): 4412-4422,…

Discrete Mathematics · Computer Science 2023-05-26 Shuhui Yu , Lijun Ji