In this paper, we investigate the structure of double cyclic codes of length (α,β) over R=F4+ϱF4,ϱ2=0 and give a minimal spanning set of double cyclic codes. Moreover, we extend this study to construct DNA codes from R-double c...
Let R=F4+uF4,withu2=u and S=F4+uF4+vF4,withu2=u,v2=v,uv=vu=0. In this paper, we study F4RS-cyclic codes of block length (α,β,γ) and construct cyclic DNA codes from them. F4RS-cyclic codes can be viewed as S[x]-submodules of Fq[x]&lan...
This paper considers three kinds of quasi-cyclic codes of index two with one generator or two generators and their applications in quantum code construction. In accordance with the algebraic structure of linear codes, we determine the lower bounds of...
Quasi-cyclic codes of index 3 over finite fields are studied. We give a classification of such codes. Their duals with respect to the Euclidean and Hermitian inner products are investigated. We give a characterization of self-orthogonal and dual-cont...
We study cyclic codes over the ring H of order 4 and characteristic 2 defined by generators and relations as H=⟨a,b∣2a=2b=0,a2=0,b2=b,ab=ba=0⟩. This is the first time that cyclic codes over a non-unitary ring are studied. Every cy...
Flag codes that are orbits of a cyclic subgroup of the general linear group acting on flags of a vector space over a finite field, are called cyclic orbit flag codes. In this paper, we present a new contribution to the study of such codes, by focusin...
In this paper, we investigate cyclic codes over the ring E of order 4 and characteristic 2 defined by generators and relations as E=⟨a,b∣2a=2b=0,a2=a,b2=b,ab=a,ba=b⟩. This is the first time that cyclic codes over the ring E are st...
Let R be a Galois ring, GR(pn,r), of characteristic pn and of order pnr. In this article, we study cyclic codes of arbitrary length, N, over R. We use discrete Fourier transform (DFT) to determine a unique representation of cyclic codes of length, N,...
In this note, we study skew cyclic and skew constacyclic codes over the mixed alphabet R=FqR1R2, where q=pm, p is an odd prime with m odd and R1=Fq+uFq with u2=u, and R2=Fq+uFq+vFq with u2=u,v2=v,uv=vu=0. Such codes consist of the juxtaposition of th...
Let Fq be a field of order q, where q is a power of an odd prime p, and α and β are two non-zero elements of Fq. The primary goal of this article is to study the structural properties of cyclic codes over a finite ring R=Fq[u1,u2]/⟨...
The soft decision decoding algorithm for cyclic codes, especially the maximum likelihood (ML) decoding algorithm, can obtain significant performance superior to that of algebraic decoding, but the complexity is much higher. To deal with this problem,...
The key objective of this paper is to study the cyclic codes over mixed alphabets on the structure of FqPQ, where P=Fq[v]⟨v3−α22v⟩ and Q=Fq[u,v]⟨u2−α12,v3−α22v⟩ are nonchain finite rings...
Let e be a fixed positive integer and n1,n2 be odd positive integers. The main objective of this article is to investigate the algebraic structure of double cyclic codes of length (n1,n2) over the finite chain ring Re = F4e+vF4e, where v2=0...
In this article, we investigate the formation of reversible cyclic codes (i.e., its codewords forms a symmetry) over the ring S=F2+uF2+u2F2, where u3=0. We find a unique set of generators for cyclic codes over S and classify reversible cyclic codes t...
In recent years, network coding has attracted widespread attention due to its important role in digital communication and network security. Among these, cyclic subspace codes have very important applications in error correction and rectification in r...
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection, error correction, data transmission, and data storage. Codes are studied...
Let p be a prime number and m be a positive integer. In this paper, we investigate cyclic codes of length n over the local non-Frobenius ring R=GR(p2,m)[u], where u2=0 and pu=0. We first determine the algebraic structure of cyclic codes of arbitrary...
In this paper, an algebraic structure of a type of double cyclic codes is investigated, which covers some existing codes as special cases. The paper presents generic results about the generating polynomials, minimal generating sets, matrices and dual...
Let p be a prime and Fp a finite field of order p. This paper investigates cyclic codes over the ring Rp2,u=Zp2+uZp2 of order p4, where the nilpotent element u satisfies u2=0 and pu≠0. The condition u2=0 with pu≠0 is crucial, as it creates a no...
Let Fq be a finite field with an odd characteristic. In this paper, we present a new result about double cyclic codes over a finite non-chain ring. Specifically, we study the double cyclic code over Fq+vFq+v2Fq with v3=v, which is isomorphic to Fq&ti...
The present study examines the application of interactive software models for training on the topic of “Cyclic Codes” in order to increase the success rate and engagement of students in technical disciplines. Two models have been develope...
In this paper, we propose a finite alphabet iterative decoder (FAID) named rate-compatible mutual-information-maximizing quantized shuffled min-sum (RC-MIM-QSMS) decoder, for decoding quasi-cyclic low-density parity-check (QC-LDPC) codes with various...
Entanglement-assisted quantum-error-correcting (EAQEC) codes are quantum codes which use entanglement as a resource. These codes can provide better error correction than the (entanglement unassisted) codes derived from the traditional stabilizer form...
The main motivation of this work is to study and obtain some reversible and DNA codes of length n with better parameters. Here, we first investigate the structure of cyclic and skew cyclic codes over the chain ring R:=F4[v]/⟨v3⟩. We sho...
An effective construction method for long-length quantum code has important applications in the field based on large-scale data. With the rapid development of quantum computing, how to construct this class of quantum coding has become one of the key...
The problem of the existence of optimal (v,k,1) binary cyclically permutable constant-weight (CPCW) codes has been completely solved for codeword weights k<5. We consider the smallest open cases, namely k=5 and k=6. We present such codes for small...
We propose a distributed quasi-cyclic low-density parity-check (QC-LDPC) coded spatial modulation (D-QC-LDPCC-SM) scheme with source, relay and destination nodes. At the source and relay, two distinct QC-LDPC codes are used. The relay chooses partial...
In this note, the following basic question is explored: in a cyclic group, how are the Shannon entropies of the sum and difference of i.i.d. random variables related to each other? For the integer group, we show that they can differ by any real numbe...
The design of a practical code-based signature scheme is an open problem in post-quantum cryptography. This paper is the full version of a work appeared at SIN’18 as a short paper, which introduced a simple and efficient one-time secure signatu...
In this article, we consider a semi-local ring S=Fq+uFq, where u2=u, q=ps and p is a prime number. We define a multiplication yb=β(b)y+γ(b), where β is an automorphism and γ is a β-derivation on S so that S[y;β,γ...
We recall a classic lower bound on the minimum Hamming distance of constacyclic codes over finite fields, analogous to the well-known BCH bound for cyclic codes. This BCH-like bound serves as a foundation for proposing some minimum-distance lower bou...
Let k,m be positive integers and F2m be a finite field of order 2m of characteristic 2. The primary goal of this paper is to study the structural properties of cyclic codes over the ring Sk=F2m[v1,v2,…,vk]⟨vi2−αivi,vivj&minu...
In modern communication systems, the concatenation of a low-density parity-check (LDPC) code with a cyclic redundancy check (CRC) code is commonly used for error correction. In this paper, we propose a low-complexity two-stage scheme for decoding the...
The guessing number of a digraph is a new invariant in graph theory raised by S. Riis in 2006 and based on its applications in network coding and boolean circuit complexity theory. In this paper, we present the lower and upper bounds on a guessing nu...
A methodology for determining the cyclic variability in spark-ignition (SI) engines has been developed recently, with the use of an in-house computational fluid dynamics (CFD) code. The simulation of a large number of engine cycles is required for th...
ASME and RCC-M codes specify an elastoplastic fatigue analysis technique: a simplified elastoplastic fatigue analysis method based on linear elastic analysis. In this method, the elastic strain range is multiplied by the elastoplastic correction fact...
This paper presents a novel efficient encoding method and a high-throughput low-complexity encoder architecture for quasi-cyclic low-density parity-check (QC-LDPC) codes for the 5th-generation (5G) New Radio (NR) standard. By storing the quantized va...
Non-orthogonal multiple access (NOMA) is the technique proposed for multiple access in the fifth generation (5G) cellular network. In NOMA, different users are allocated different power levels and are served using the same time/frequency resource blo...
This work presents a novel fully parallel decoder architecture designed for high-throughput decoding of Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes within the context of 5G New-Radio (NR) communication. The design uses the layered Min-Sum (...
Next generation sequencing of RNA molecules (RNA-seq) has become a common tool to characterize the expression profiles of RNAs and their regulations in normal physiological processes and diseases. Although increasingly accumulating RNA-seq data are w...
In the context of Internet of Things and 5G communication, ensuring the accuracy and reliability of data transmission is critical, especially as the future 6G communication system places a greater emphasis on highly reliable transmission. However, th...
Coding of biological information is not confined to nucleic acids and proteins. Endowed with the highest level of structural versatility among biomolecules, the glycan chains of cellular glycoconjugates are well-suited to generate molecular messages/...
In this paper, we study the structural properties of ( α + u 1 β + u 2 γ + u 1 u 2 δ ) -constacyclic codes over R = F q [ u 1 , u 2 ] / ⟨ u 1 2 − u 1 , u 2 2 − u 2 , u 1 u...
The construction of self-dual and linear complementary dual (LCD) codes over finite rings, particularly over semi-local and local structures, is an active area of research due to their algebraic richness and applications in communications and cryptog...
This paper presents a pipelined layered quasi-cyclic low-density parity-check (QC-LDPC) decoder architecture targeting low-complexity, high-throughput, and efficient use of hardware resources compliant with the specifications of 5G new radio (NR) wir...
In this study, we consider codes over Euclidean domains modulo their ideals. In the first half of the study, we deal with arbitrary Euclidean domains. We show that the product of generator matrices of codes over the rings mod a and mod b produces gen...
A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the ensemble of c...
In this paper, new construction methods of entanglement-assisted quantum error correction code (EAQECC) from circulant matrices are proposed. We first construct the matrices from two vectors of constraint size, and determine the isotropic subgroup. T...
When concrete is subjected to cycles of compression, its strength is lower than the statically determined concrete compressive strength. This reduction is typically expressed as a function of the number of cycles. In this work, we study the reduced c...
Towards the era of mobile Internet and the Internet of Things (IoT), numerous sensors and devices are being introduced and interconnected. To support such an amount of data traffic, traditional wireless communication technologies are facing challenge...
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