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Electronic Colloquium on Computational Complexity

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All reports by Author Sivakanth Gopi:

TR17-183 | 28th November 2017
Sivakanth Gopi, Venkatesan Guruswami, Sergey Yekhanin

On Maximally Recoverable Local Reconstruction Codes

In recent years the explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Local Reconstruction Codes (LRCs) have emerged as the codes of choice for these applications. An $(n,r,h,a,q)$-LRC is a $q$-ary code, where encoding is as a ... more >>>

TR16-189 | 21st November 2016
Arnab Bhattacharyya, Sivakanth Gopi

Lower bounds for 2-query LCCs over large alphabet

A locally correctable code (LCC) is an error correcting code that allows correction of any arbitrary coordinate of a corrupted codeword by querying only a few coordinates.
We show that any zero-error $2$-query locally correctable code $\mathcal{C}: \{0,1\}^k \to \Sigma^n$ that can correct a constant fraction of corrupted symbols must ... more >>>

TR16-122 | 11th August 2016
Sivakanth Gopi, Swastik Kopparty, Rafael Mendes de Oliveira, Noga Ron-Zewi, Shubhangi Saraf

Locally testable and Locally correctable Codes Approaching the Gilbert-Varshamov Bound

One of the most important open problems in the theory
of error-correcting codes is to determine the
tradeoff between the rate $R$ and minimum distance $\delta$ of a binary
code. The best known tradeoff is the Gilbert-Varshamov bound,
and says that for every $\delta \in (0, 1/2)$, there are ... more >>>

TR15-185 | 24th November 2015
Arnab Bhattacharyya, Sivakanth Gopi

Lower bounds for constant query affine-invariant LCCs and LTCs

Affine-invariant codes are codes whose coordinates form a vector space over a finite field and which are invariant under affine transformations of the coordinate space. They form a natural, well-studied class of codes; they include popular codes such as Reed-Muller and Reed-Solomon. A particularly appealing feature of affine-invariant codes is ... more >>>

TR14-094 | 24th July 2014
Zeev Dvir, Sivakanth Gopi

2-Server PIR with sub-polynomial communication

A 2-server Private Information Retrieval (PIR) scheme allows a user to retrieve the $i$th bit of an $n$-bit database replicated among two servers (which do not communicate) while not revealing any information about $i$ to either server. In this work we construct a 1-round 2-server PIR with total communication cost ... more >>>

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