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We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum…

Information Theory · Computer Science 2019-02-15 Carlos Galindo , Fernando Hernando , Ryutaroh Matsumoto

The minimum distance of expander codes over GF(q) is studied. A new upper bound on the minimum distance of expander codes is derived. The bound is shown to lie under the Varshamov-Gilbert (VG) bound while q >= 32. Lower bounds on the…

Information Theory · Computer Science 2011-06-01 Alexey Frolov , Victor Zyablov

We construct linear codes over the finite field Fq from arbitrary simplicial complexes, establishing a connection between topological properties and fundamental coding parameters. First, we study the behaviour of the weights of codewords…

Information Theory · Computer Science 2026-03-05 Antonio Jesús Lorite López , Daniel Camazón Portela , Juan Antonio López Ramos

In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…

Information Theory · Computer Science 2022-01-03 Yansheng Wu , Chengju Li , Fu Xiao

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…

Information Theory · Computer Science 2014-03-12 Bocong Chen , San Ling , Guanghui Zhang

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

Recently, some infinite families of binary minimal and optimal linear codes are constructed from simplicial complexes by Hyun {\em et al}. Inspired by their work, we present two new constructions of codes over the ring $\Bbb F_2+u\Bbb F_2$…

Information Theory · Computer Science 2019-10-11 Yansheng Wu , Xiaomeng Zhu , Qin Yue

In this work, we define three composite matrices derived from group rings. We employ these composite matrices to create generator matrices of the form [In | {\Omega}(v)], where In is the identity matrix and {\Omega}(v) is a composite matrix…

Information Theory · Computer Science 2021-02-02 Adrian Korban , Serap Sahinkaya , Deniz Ustun

A code is said to be two-weight if the non-zero codewords have only two different a weight w1 and w2. Two-weight codes are closely related to strongly regular graphs. In this paper. It is shown that a consta-cyclic code of composite length…

Information Theory · Computer Science 2009-01-12 Eric Z. Chen

This paper proposes a new family of recursive systematic convolutional codes, defined in the non-binary domain over different Galois fields GF(q) and intended to be used as component codes for the design of non-binary turbo codes. A general…

Information Theory · Computer Science 2018-07-23 Rami Klaimi , Charbel Abdel Nour , Catherine Douillard , Joumana Farah

In this paper we investigate linear codes with complementary dual (LCD) codes and formally self-dual codes over the ring $R=\F_{q}+v\F_{q}+v^{2}\F_{q}$, where $v^{3}=v$, for $q$ odd. We give conditions on the existence of LCD codes and…

Information Theory · Computer Science 2017-04-13 A. Melakhessou , K. Guenda , T. A. Gulliver , M. Shi , P. Solé

It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and…

Information Theory · Computer Science 2019-12-06 Weijun Fang , Fang-Wei Fu

In this paper, we present a new bordered construction for self-dual codes which employs $\lambda$-circulant matrices. We give the necessary conditions for our construction to produce self-dual codes over a finite commutative Frobenius ring…

Information Theory · Computer Science 2023-03-24 Joe Gildea , Adrian Korban , Adam Michael Roberts , Alexander Tylyshchak

Self-orthogonal codes are a significant class of linear codes in coding theory and have attracted a lot of attention. In \cite{HLL2023Te,LH2023Se}, $p$-ary self-orthogonal codes were constructed by using $p$-ary weakly regular bent…

Information Theory · Computer Science 2024-03-20 Jiaxin Wang , Yadi Wei , Fang-Wei Fu , Juan Li

It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…

Quantum Physics · Physics 2007-05-23 Eric M. Rains

Two classes of turbo codes over high-order finite fields are introduced. The codes are derived from a particular protograph sub-ensemble of the (dv=2,dc=3) low-density parity-check code ensemble. A first construction is derived as a…

Information Theory · Computer Science 2016-11-17 Gianluigi Liva , Enrico Paolini , Sandro Scalise , Marco Chiani

In this work, quadratic double and quadratic bordered double circulant constructions are applied to F_4 + uF_4 as well as F_4, as a result of which extremal binary self-dual codes of length 56 and 64 are obtained. The binary extension…

Combinatorics · Mathematics 2016-02-25 Abidin Kaya , Bahattin Yildiz , Irfan Siap

We give a polynomial representation for additive cyclic codes over $\mathbb{F}_{p^2}$. This representation will be applied to uniquely present each additive cyclic code by at most two generator polynomials. We determine the generator…

Information Theory · Computer Science 2023-01-03 Reza Dastbasteh , Khalil Shivji

Let $\mathbb{F}_q$ be a finite field with $q=p^{e}$ elements, where $p$ is a prime number and $e \geq 1$ is an integer. In this paper, by means of generalized Reed-Solomon (GRS) codes, we construct two new classes of quantum…

Information Theory · Computer Science 2020-02-17 Hualu Liu , Xiusheng Liu

Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder…

Information Theory · Computer Science 2017-02-02 Cem Güneri , Ferruh Özbudak , Buket Özkaya , Elif Saçıkara , Zahra Sepasdar , Patrick Solé
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