Related papers: An efficient implementation of the Shamir secret s…
Codes over rings, especially over Galois rings, have been extensively studied for nearly three decades due to their similarity to linear codes over finite fields. A distributed storage system uses a linear code to encode a large file across…
For the majority of the applications of Reed-Solomon (RS) codes, hard decision decoding is based on syndromes. Recently, there has been renewed interest in decoding RS codes without using syndromes. In this paper, we investigate the…
In this work, we introduce a new technique for taking a single-secret sharing scheme with a general access structure and transforming it into an individually secure multi-secret sharing scheme where every secret has the same general access…
Due to dependence between codeword elements, index modulation (IM) and related modulation techniques struggle to provide simple solutions for practical problems such as Gray coding between information bits and constellation points; and…
In this paper we address the problem of decoding linearized Reed-Solomon (LRS) codes beyond their unique decoding radius. We analyze the complexity in order to evaluate if the considered problem is of cryptographic relevance, i.e., can be…
A construction of Partial Maximum Distance Separable (PMDS) and Sector-Disk (SD) codes extending RAID 5 with two extra parities is given, solving an open problem. Previous constructions relied on computer searches, while our constructions…
A (t,n)-threshold secret sharing scheme is a method to distribute a secret among n participants in such a way that any t participants can recover the secret, but no t-1 participants can. In this paper, we propose two secret sharing schemes…
Near MDS (NMDS) codes are closely related to interesting objects in finite geometry and have nice applications in combinatorics and cryptography. But there are many unsolved problems about construction of NMDS codes. In this paper, by using…
There are different ways to realize Reed Solomon (RS) codes. While in the storage community, using the generator matrices to implement RS codes is more popular, in the coding theory community the generator polynomials are typically used to…
We study the existence over small fields of Maximum Distance Separable (MDS) codes with generator matrices having specified supports (i.e. having specified locations of zero entries). This problem unifies and simplifies the problems posed…
We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them…
We analyze whether a multidimensional parity check (MDPC) or a Reed-Solomon (RS) code in combination with an auxiliary channel can improve the throughput and extend the THz transmission distance. While channel quality is addressed by…
The PRRT protocol enables applications with strict performance requirements such as Cyber-Physical Systems, as it provides predictably low, end-to-end delay via cross-layer pacing and timely error correction via Hybrid ARQ (HARQ). However,…
We derive a lower bound on the amount of information accessed to repair failed nodes within a single rack from any number of helper racks in the rack-aware storage model that allows collective information processing in the nodes that share…
This paper presents MULTISS, a new protocol for long-term storage distributed across multiple Quantum Key Distribution (QKD) networks. This protocol is an extension of LINCOS, a secure storage protocol that uses Shamir secret sharing for…
Maximum distance separable (in short, MDS), near MDS (in short, NMDS), and self-orthogonal codes play a pivotal role in algebraic coding theory, particularly in applications such as quantum communications and secret sharing scheme.…
Remote sensing (RS) images are usually stored in compressed format to reduce the storage size of the archives. Thus, existing content-based image retrieval (CBIR) systems in RS require decoding images before applying CBIR (which is…
We study linear codes that maximize minimum distance subject to arbitrary support constraints on the parity-check matrix. Such constraints arise naturally in the design of LDPC codes, locally repairable codes, and hardware-constrained…
A linear code with parameters $[n, k, n-k+1]$ is called a maximum distance separable (MDS for short) code. A linear code with parameters $[n, k, n-k]$ is said to be almost maximum distance separable (AMDS for short). A linear code is said…
In this paper, we investigate maximum distance separable (MDS) codes based group coded caching in fog radio access networks (F-RANs). The goal is to minimize the average fronthaul rate under nonuniform file popularity. Firstly, an MDS codes…