ﻻ يوجد ملخص باللغة العربية
This paper presents the construction of an explicit, optimal-access, high-rate MSR code for any $(n,k,d=k+1,k+2,k+3)$ parameters over the finite field $fQ$ having sub-packetization $alpha = q^{lceilfrac{n}{q}rceil}$, where $q=d-k+1$ and $Q = O(n)$. The sub-packetization of the current construction meets the lower bound proven in a recent work by Balaji et al. in cite{BalKum}. To our understanding the codes presented in this paper are the first explicit constructions of MSR codes with $d<(n-1)$ having optimal sub-packetization, optimal access and small field size.
Streaming codes are a class of packet-level erasure codes that ensure packet recovery over a sliding window channel which allows either a burst erasure of size $b$ or $a$ random erasures within any window of size $(tau+1)$ time units, under a strict
An $(n, M)$ vector code $mathcal{C} subseteq mathbb{F}^n$ is a collection of $M$ codewords where $n$ elements (from the field $mathbb{F}$) in each of the codewords are referred to as code blocks. Assuming that $mathbb{F} cong mathbb{B}^{ell}$, the co
This paper addresses the problem of constructing MDS codes that enable exact repair of each code block with small repair bandwidth, which refers to the total amount of information flow from the remaining code blocks during the repair process. This pr
We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic regimes, the
We consider multi-access coded caching problem introduced by Hachem et.al., where each user has access to $L$ neighboring caches in a cyclic wrap-around fashion. We focus on the deterministic schemes for a specific class of multi-access coded caching