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Spatially-coupled (SC) LDPC codes have recently emerged as an excellent choice for error correction in modern data storage and communication systems due to their outstanding performance. It has long been known that irregular graph codes…
In this paper, we give a generalization on the error correcting capability of twisted centralizer codes obtained from a fixed rank 1 matrix. In particular, we fix the combinatorial matrix which is obtained by getting the linear combination…
An $(r,M,2\delta;k)_q$ constant--dimension subspace code, $\delta >1$, is a collection $\cal C$ of $(k-1)$--dimensional projective subspaces of ${\rm PG(r-1,q)}$ such that every $(k-\delta)$--dimensional projective subspace of ${\rm…
Coding in the projective space has received recently a lot of attention due to its application in network coding. Reduced row echelon form of the linear subspaces and Ferrers diagram can play a key role for solving coding problems in the…
The rank metric measures the distance between two matrices by the rank of their difference. Codes designed for the rank metric have attracted considerable attention in recent years, reinforced by network coding and further motivated by a…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
Locally recoverable (LRC) codes provide a solution to single node failure in distributed storage systems, where it is a very common problem. On the other hand, linear complementary dual (LCD) codes are useful in fault injections attacks on…
Regenerating codes and codes with locality are two schemes that have recently been proposed to ensure data collection and reliability in a distributed storage network. In a situation where one is attempting to repair a failed node,…
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…
In this paper, on one hand, a class of linear codes with one or two weights is obtained. Based on these linear codes, we construct two classes of constant composition codes, which includes optimal constant composition codes depending on…
Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding…
Random network coding recently attracts attention as a technique to disseminate information in a network. This paper considers a non-coherent multi-shot network, where the unknown and time-variant network is used several times. In order to…
One of the main problems of the research area of network coding is to compute good lower and upper bounds of the achievable cardinality of so-called subspace codes in $\operatorname{PG}(n,q)$, i.e., the set of subspaces of $\mathbb{F}_q^n$,…
This work deals with partial MDS (PMDS) codes, a special class of locally repairable codes, used for distributed storage system. We first show that a known construction of these codes, using Gabidulin codes, can be extended to use any…
In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors…
The Pl\"{u}cker coordinate description of subspaces has been recently discussed in the context of constant dimension subspace codes for random networks, as well as the Schubert cell description of certain code parameters. In this paper this…
The locally repairable codes (LRCs) were introduced to correct erasures efficiently in distributed storage systems. LRCs are extensively studied recently. In this paper, we first deal with the open case remained in \cite{q} and derive an…
A new construction for constant weight codes is presented. The codes are constructed from $k$-dimensional subspaces of the vector space $\F_q^n$. These subspaces form a constant dimension code in the Grassmannian space $\cG_q(n,k)$. Some of…
Sum-rank metric codes, as a generalization of Hamming codes and rank metric codes, have important applications in fields such as multi-shot linear network coding, space-time coding and distributed storage systems. The purpose of this study…
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.