Nested linear coding is a widely used technique in wireless communication systems for improving both security and reliability. Some parameters, such as the relative generalized Hamming weight and the relative dimension/length profile, can be used to...
A modification of the Brouwer–Zimmermann algorithm for calculating the minimum weight of a linear code over a finite field is presented. The aim was to reduce the number of codewords for consideration. The reduction is significant in cases where the...
The hull of a linear code C is the intersection of C with its dual code. The goal is to study the dimensions of the hulls of optimal binary and ternary linear codes for a given length and dimension. The focus is on the lengths at which self-orthogona...
Sunflower in coding theory is a class of important subspace codes and can be used to construct linear codes. In this paper, we study the minimality of linear codes over
This work studies projective self-dual (PSD) and self-polar linear codes over finite fields with q elements, where q is a power of a prime. The possible parameters for which PSD codes may exist are presented, and many examples are provided. Algorithm...
A classical reduced order model (ROM) for dynamical problems typically involves only the spatial reduction of a given problem. Recently, a novel space–time ROM for linear dynamical problems has been developed [Choi et al., Space–tume reduced order mo...
Bounds for the parameters of codes are very important in coding theory. The Grey–Rankin bound refers to the cardinality of a self-complementary binary code. Codes meeting this bound are associated with families of two-weight codes and other com...
This paper presents a coding theorem for linear coding over finite rings, in the setting of the Slepian–Wolf source coding problem. This theorem covers corresponding achievability theorems of Elias (IRE Conv. Rec. 1955, 3, 37–46) and Csiszár (IEEE Tr...
In this paper, we design and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. The advantage of using these codes is that they have the ability to transmit m-distinct messages to m-set of receivers...
In this paper, we put forward the model of multiple linear-combination security multicast network coding, where the wiretapper desires to obtain some information about a predefined set of multiple linear combinations of the source symbols by eavesdro...
An algorithm for equivalence of linear codes over finite fields is presented. Its main advantage is that it can extract exactly one representative from each equivalence class among a large number of linear codes. It can also be used as a test for iso...
In hybrid block-based video coding, transform plays an important role in energy compaction. Transform coding converts residual data in the spatial domain into frequency domain data, thereby concentrating energy in a lower frequency band. In VVC (vers...
The algebraic analysis of linear code parameters reveals deep connections with cryptographic constructions, including the Information Dispersal Algorithms (IDAs) and secret-sharing schemes. In this work, we propose an algebraic method for constructin...
The optimal security parameters for binary linear complementary pair (LCP) codes are open. Inspired by this, we study LCPs of codes. In this paper, we construct two families of optimal binary LCPs of codes.
Linear codes with a few weights have been extensively studied due to their wide applications in secret sharing schemes, strongly regular graphs, association schemes, and authentication codes. In this paper, we choose the defining sets from two distin...
Compared with scalar linear network coding (LNC) formulated over the finite field GF(
Linear codes are the most important family of codes in cryptography and coding theory. Some codes only have a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs. By setting...
This paper presents a lossless image compression method with a fast decoding time and flexible adjustment of coder parameters affecting its implementation complexity. A comparison of several approaches for computing non-MMSE prediction coefficients w...
In this paper, we propose a novel deep learning-based framework for the joint design and decoding of linear block codes, the end-to-end deep coding cross-attention message-passing Transformer (E2E DC-CrossMPT). To improve linear block code design and...
Recent works have combined random linear network coding (RLNC) with guessing random additive noise decoding (GRAND) to leverage RLNC packets to partially correct bit errors prior to RLNC decoding, so as to reduce the packet erasure rates in wireless...
As far as taking-away of the symmetry constraints is concerned, as a scientifically symmetry problem, the global synthesis for antenna arrays that produce the desired radiation pattern is also a highly nonlinear optimization issue in fact. Besides th...
To improve coding efficiency by exploiting the local inter-component redundancy between the luma and chroma components, the cross-component linear model (CCLM) is included in the versatile video coding (VVC) standard. In the CCLM mode, linear model p...
Aiming to solve the problem of the distinction of scrambled linear block codes, a method for identifying the scrambling types of linear block codes by combining correlation features and convolution long short-term memory neural networks is proposed i...
The conventional soft decision decoding (SDD) methods require various hard decision decoders (HDDs) based on different codes or re-manipulate the generator matrix by the complicated Gaussian elimination technique according to the bit reliability. Thi...
We design a decoding algorithm for linear codes over finite chain rings given by their parity check matrices. It is assumed that decoding algorithms over the residue field are known at each degree of the adic decomposition.
Programming activities have the potential to provide a rich context for exploring measurement units in early elementary mathematics. This study examines how a small group of young children (ages 5–6) express their emergent conception of a dynam...
In this article, we present a technique that allows us to generate parallel tiled code to calculate general linear recursion equations (GLRE). That code deals with multidimensional data and it is computing-intensive. We demonstrate that data dependen...
We present a parallel algorithm for computing the covering radius of a linear
In the era of the Internet of Things, there are many applications where numerous devices are deployed to acquire information and send it to analyse the data and make informed decisions. In these applications, the power consumption and price of the de...
The new generation video coding standard Versatile Video Coding (VVC) has adopted many novel technologies to improve compression performance, and consequently, remarkable results have been achieved. In practical applications, less data, in terms of b...
An exponential increase in mobile video delivery will continue with the demand for higher resolution, multi-view and large-scale multicast video services. Novel fifth generation (5G) 3GPP New Radio (NR) standard will bring a number of new opportuniti...
We discuss the effect of sequential error injection on information leakage under a network code. We formulate a network code for the single transmission setting and the multiple transmission setting. Under this formulation, we show that the eavesdrop...
Human behavior recognition technology is widely adopted in intelligent surveillance, human–machine interaction, video retrieval, and ambient intelligence applications. To achieve efficient and accurate human behavior recognition, a unique appro...
Fenestration systems play a critical role in building thermal performance, particularly in cooling-dominated climates where envelope inefficiencies directly amplify electricity demand. In Saudi Arabia and other Gulf Cooperation Council (GCC) countrie...
For a finite field GF(
Vehicle-to-vehicle (V2V) communication has gained significant attention in the field of intelligent transportation systems. In this paper, we focus on communication scenarios involving vehicles moving in the same and opposite directions. Specifically...
Monitoring the condition of rolling bearings is a crucial task in many industries. An efficient tool for diagnosing bearing defects is necessary since they can lead to complete machine failure and significant economic losses. Traditional diagnosis so...
We consider combinatorial multi-access coded caching with private caches, where users are connected to two types of caches: private caches and multi-access caches. Each user has its own private cache, while multi-access caches are connected in the sa...
Considering the significance of an energy efficient, delay tolerant and reliable communication protocol for underwater acoustic wireless sensor network (UWSN), this paper proposes a novel systematic random linear network coding (SRLNC) based transmis...
The superiority of a global navigation satellite system (GNSS)/inertial navigation system (INS) ultra-tight integration navigation system has been widely verified. For those systems with centralized structure based on coherent-accumulation measuremen...
While the use of steel hysteretic dampers has spread in the last decade for both new and retrofitted constructions, the Italian Building Code (IBC), as well as the Eurocode 8, does not provide specific recommendations for the design and verification...
It is an important issue to search for self-orthogonal codes for construction of quantum codes by CSS construction (Calderbank-Sho-Steane codes); in quantum error correction, CSS codes are a special type of stabilizer codes constructed from classical...
Linear complementary dual (LCD) codes, which are a class of linear codes introduced by Massey, have been extensively studied in the literature recently. It has been shown that LCD codes play a role in measures to counter passive and active side-chann...
Systematic codes are of important practical interest for communications. Network coding, however, seems to conflict with systematic codes: although the source node can transmit message packets, network coding at the intermediate network nodes may sig...
Vectorial Boolean functions and codes are closely related and interconnected. On the one hand, various requirements of binary linear codes are needed for their theoretical interests but, more importantly, for their practical applications (such as few...
Speech compression is a key technology underlying digital cellular communications, VoIP, voicemail, and voice response systems. We trace the evolution of speech coding based on the linear prediction model, highlight the key milestones in speech codin...
We introduce some methods for constructing quaternary Hermitian self-orthogonal (HSO) codes, and construct quaternary
In this paper, an index-coded Automatic Repeat Request (ARQ) is studied in the perspectives of transmission efficiency and memory overhead. Motivated by reducing significant computational complexity from huge matrix inverse computation of random line...
The use of error-correcting codes (ECCs) is essential for designing reliable digital communication systems. Usually, most systems correct errors under cooperative environments. If receivers do not know interleaver parameters, they must first find out...
Inspired by the concept of
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