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We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Recently, linear codes with few weights have been widely studied, since they have applications in data storage systems, communication systems and consumer electronics. In this paper, we present a class of three-weight and five-weight linear…
Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime power $q$, we construct some class of linear code over finite field $\mathbb{F}_q$ with defining set be the preimage of…
The structure of a linear block code is pivotal in defining fundamental properties, particularly weight distribution, and code design. In this study, we characterize the Type II structure of polar codewords with weights less than twice the…
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…
Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…
Under the emerging network coding paradigm, intermediate nodes in the network are allowed not only to store and forward packets but also to process and mix different data flows. We propose a low-complexity cryptographic scheme that exploits…
We study the properties of secret sharing schemes, where a random secret value is transformed into shares distributed among several participants in such a way that only the qualified groups of participants can recover the secret value. We…
As a special class of linear codes, minimal linear codes have important applications in secret sharing and secure two-party computation. Constructing minimal linear codes with new and desirable parameters has been an interesting research…
Recently, minimal linear codes have been extensively studied due to their applications in secret sharing schemes, two-party computations, and so on. Constructing minimal linear codes violating the Ashikhmin-Barg condition and then…
Weak superimposed codes are combinatorial structures related closely to generalized cover-free families, superimposed codes, and disjunct matrices in that they are only required to satisfy similar but less stringent conditions. This class…
Recently, simplicial complexes are used in constructions of several infinite families of minimal and optimal linear codes by Hyun {\em et al.} Building upon their research, in this paper more linear codes over the ring $\mathbb{Z}_4$ are…
Linear codes with few weights have been a significant area of research in coding theory for many years, due to their applications in secret sharing schemes, authentication codes, association schemes, and strongly regular graphs. Inspired by…
In this paper, we propose a class of linear codes and obtain their weight distribution. Some of these codes are almost optimal. Moreover, several classes of constant composition codes(CCCs) are constructed as subcodes of linear codes.
Recently some mixed alphabet rings are involved in constructing few-Lee weight additive codes with optimal or minimal Gray images using suitable defining sets or down-sets. Inspired by these works, we choose the mixed alphabet ring…
We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly…
Linear codes with a few weights have been widely investigated in recent years. In this paper, we mainly use Gauss sums to represent the Hamming weights of a class of $q$-ary linear codes under some certain conditions, where $q$ is a power…
The puncturing and shortening technique are two important approaches to constructing new linear codes from old ones. In the past 70 years, a lot of progress on the puncturing technique has been made, and many works on punctured linear codes…
Network coding provides the advantage of maximizing the usage of network resources, and has great application prospects in future network communications. However, the properties of network coding also make the pollution attack more serious.…
Linear codes with a few weights are an important class of codes in coding theory and have attracted a lot of attention. In this paper, we present several constructions of $q$-ary linear codes with two or three weights from vectorial…