Related papers: Constructions of Batch Codes via Finite Geometry
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
Batch codes are a useful notion of locality for error correcting codes, originally introduced in the context of distributed storage and cryptography. Many constructions of batch codes have been given, but few lower bound (limitation)…
The binary $k$-dimensional simplex code is known to be a $2^{k-1}$-batch code and is conjectured to be a $2^{k-1}$-functional batch code. Here, we offer a simple, constructive proof of a result that is "in between" these two properties. Our…
Batch codes are a type of codes specifically designed for coded distributed storage systems and private information retrieval protocols. These codes have got much attention in recent years due to their ability to enable efficient and secure…
Batch codes are of potential use for load balancing and private information retrieval in distributed data storage systems. Recently, a special case of batch codes, termed functional batch codes, was proposed in the literature. In functional…
We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…
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…
Circuit codes are constructed from induced cycles in the graph of the $n$ dimensional hypercube. They are both theoretically and practically important, as circuit codes can be used as error correcting codes. When constructing circuit codes,…
Linear codes are widely employed in communication systems, consumer electronics, and storage devices. All linear codes over finite fields can be generated by a generator matrix. Due to this, the generator matrix approach is called a…
Affine Cartesian codes are defined by evaluating multivariate polynomials at a cartesian product of finite subsets of a finite field. In this work we examine properties of these codes as batch codes. We consider the recovery sets to be…
Neural codes are collections of binary strings motivated by patterns of neural activity. In this paper, we study algorithmic and enumerative aspects of convex neural codes in dimension 1 (i.e. on a line or a circle). We use the theory of…
In this short survey we concern ourselves with minimal codes, a classical object in coding theory. We will explain the relation between minimal codes and various other mathematical domains, in particular with finite projective geometry.…
Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…
We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we…
We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSS-type construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum…
Various types of recovery algorithms for batch codes have been investigated, such as asynchronous recovery or recovery as afforded by batch codes obtained from Almost Affinely Disjoint (AAD) families. In this paper, we offer the first…
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…
In coding theory, codes are usually designed with a certain level of randomness to facilitate analysis and accommodate different channel conditions. However, the resulting random code constructed can be suboptimal in practical…
Recently, many good quantum codes over various finite fields $F_q$ have been constructed from codes over extension rings or mixed alphabet rings via some version of a Gray map. We show that most of these codes can be obtained more directly…