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Minimum storage regenerating (MSR) codes are MDS codes which allow for recovery of any single erased symbol with optimal repair bandwidth, based on the smallest possible fraction of the contents downloaded from each of the other symbols. Recently, certain Reed-Solomon codes were constructed which are MSR. However, the sub-packetization of these codes is exponentially large, growing like $n^{Omega(n)}$ in the constant-rate regime. In this work, we study the relaxed notion of $epsilon$-MSR codes, which incur a factor of $(1+epsilon)$ higher than the optimal repair bandwidth, in the context of Reed-Solomon codes. We give constructions of constant-rate $epsilon$-MSR Reed-Solomon codes with polynomial sub-packetization of $n^{O(1/epsilon)}$ and thereby giving an explicit tradeoff between the repair bandwidth and sub-packetization.
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
In this article we count the number of generalized Reed-Solomon (GRS) codes of dimension k and length n, including the codes coming from a non-degenerate conic plus nucleus. We compare our results with known formulae for the number of 3-dimensional MDS codes of length n=6,7,8,9.
Projective Reed-Solomon (PRS) codes are Reed-Solomon codes of the maximum possible length q+1. The classification of deep holes --received words with maximum possible error distance-- for PRS codes is an important and difficult problem. In this paper
This article discusses the security of McEliece-like encryption schemes using subspace subcodes of Reed-Solomon codes, i.e. subcodes of Reed-Solomon codes over $mathbb{F}_{q^m}$ whose entries lie in a fixed collection of $mathbb{F}_q$-subspaces of $m