Related papers: LRCs: Duality, LP Bounds, and Field Size
In this paper we investigate bounds on rate and minimum distance of codes with $t$ availability. We present bounds on minimum distance of a code with $t$ availability that are tighter than existing bounds. For bounds on rate of a code with…
In modern data storage systems, non-binary LDPC codes for recovering from disk failures are increasingly considered strong competitors to MDS codes such as Reed-Solomon codes. Since disk failures can be modeled as erasures, we analyze…
Locally decodable channel codes form a special class of error-correcting codes with the property that the decoder is able to reconstruct any bit of the input message from querying only a few bits of a noisy codeword. It is well known that…
We analyze the list-decodability, and related notions, of random linear codes. This has been studied extensively before: there are many different parameter regimes and many different variants. Previous works have used complementary styles…
We study the problem of Distributionally Robust Constrained RL (DRC-RL), where the goal is to maximize the expected reward subject to environmental distribution shifts and constraints. This setting captures situations where training and…
This work develops new foundations for the theory of linear codes over local Artinian commutative rings. We use algebraic invariants such as the socle, type, length, and minimal number of generators to measure the size of codes. We prove a…
The MacWilliams identity, which relates the weight distribution of a code to the weight distribution of its dual code, is useful in determining the weight distribution of codes. In this paper, we derive the MacWilliams identity for linear…
Two upper bounds on the minimum distance of type-1 quasi-cyclic low-density parity-check (QC LDPC) codes are derived. The necessary condition is given for the minimum code distance of such codes to grow linearly with the code length.
The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…
The cover metric is suitable for describing the resilience against correlated errors in arrays, in particular crisscross errors, which makes it interesting for applications such as distributed data storage (DDS). In this work, we consider…
Locally recoverable codes (LRCs) have emerged as fundamental objects in modern coding theory, primarily due to their pivotal role in distributed and cloud storage systems. A major breakthrough in their construction was achieved by Tamo and…
Sum-rank codes are an important class of codes which can be utilized for linear network coding, space-time coding and distributed storage. They can not only reduce the size of network alphabet but also detect and correct more errors. Based…
A non-binary (2,v)-regular LDPC code is defined by a parity-check matrix with column weight 2 and row weight v. In this report, we give an ontology-based approach to the optimization for this class of codes. All possible inter-connected…
We consider the design of regenerating codes for distributed storage systems that enjoy the property of local, exact and uncoded repair, i.e., (a) upon failure, a node can be regenerated by simply downloading packets from the surviving…
We show that locally repairable codes (LRCs) can be list decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error correction capabilities. The new decoding radius is derived and the…
We are concerned with linear redundancy storage schemes regarding their ability to provide concurrent (local) recovery of multiple data objects. This paper initiates a study of such systems within the classical coding theory. We show how we…
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…
A locally repairable code with availability has the property that every code symbol can be recovered from multiple, disjoint subsets of other symbols of small size. In particular, a code symbol is said to have $(r,t)$-availability if it can…
In this paper, we give a method for constructing linear codes with small hulls by generalizing the method in \cite{LCD-T-matric}. As a result, we obtain many optimal Euclidean LCD codes and Hermitian LCD codes, which improve the previously…
We introduce linear programs encoding regular expressions of finite languages. We show that, given a language, the optimum value of the associated linear program is a lower bound on the size of any regular expression of the language.…