Related papers: Line codes generated by finite Coxeter groups
Coding theory is a central discipline underpinning wireline and wireless modems that are the workhorses of the information age. Progress in coding theory is largely driven by individual human ingenuity with sporadic breakthroughs over the…
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…
As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and…
In this paper we study plus-one generated arrangements of conics and lines in the complex projective plane with simple singularities. We provide several degree-wise classification results that allow us to construct explicit examples of such…
We consider communication over a noisy network under randomized linear network coding. Possible error mechanism include node- or link- failures, Byzantine behavior of nodes, or an over-estimate of the network min-cut. Building on the work…
Recently, linear codes constructed by defining sets have attracted a lot of study, and many optimal linear codes with a few weights have been produced. The objective of this paper is to present a class of binary linear codes with three…
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…
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…
Linear codes with a few weights have many nice applications including combinatorial design, distributed storage system, secret sharing schemes and so on. In this paper, we construct two families of linear codes with a few weights based on…
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…
In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…
Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, linear codes…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…
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…
Let $q$ be a prime power. This paper provides a new class of linear codes that arises from the action of the alternating group on $\mathbb F_q[x_1,\dots,x_m]$ combined with the ideas in (M. Datta and T. Johnsen, 2022). Compared with…
Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
Two general constructions of linear codes with functions over finite fields have been extensively studied in the literature. The first one is given by $\mathcal{C}(f)=\left\{ {\rm Tr}(af(x)+bx)_{x \in \mathbb{F}_{q^m}^*}: a,b \in…
Batch codes serve as critical tools for load balancing in distributed storage systems. While numerous constructions exist for specific batch sizes t, current methodologies predominantly rely on code dimension parameters, limiting their…
Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of…