All reports by Author Swastik Kopparty:

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TR18-091
| 4th May 2018
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Swastik Kopparty, Noga Ron-Zewi, Shubhangi Saraf, Mary Wootters#### Improved decoding of Folded Reed-Solomon and Multiplicity Codes

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TR18-090
| 4th May 2018
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Eli Ben-Sasson, Swastik Kopparty, Shubhangi Saraf#### Worst-case to average case reductions for the distance to a code

Revisions: 1

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TR15-110
| 8th July 2015
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Swastik Kopparty, Or Meir, Noga Ron-Zewi, Shubhangi Saraf#### High-rate Locally-testable Codes with Quasi-polylogarithmic Query Complexity

Revisions: 1

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TR14-098
| 30th July 2014
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Amey Bhangale, Swastik Kopparty, Sushant Sachdeva#### Simultaneous Approximation of Constraint Satisfaction Problems

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TR13-085
| 13th June 2013
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Eli Ben-Sasson, Yohay Kaplan, Swastik Kopparty, Or Meir, Henning Stichtenoth#### Constant rate PCPs for circuit-SAT with sublinear query complexity

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TR13-060
| 10th April 2013
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Venkatesan Guruswami, Swastik Kopparty#### Explicit Subspace Designs

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TR12-149
| 8th November 2012
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Alan Guo, Swastik Kopparty, Madhu Sudan#### New affine-invariant codes from lifting

Comments: 1

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TR12-148
| 7th November 2012
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Eli Ben-Sasson, Ariel Gabizon, Yohay Kaplan, Swastik Kopparty, Shubhangi Saraf#### A new family of locally correctable codes based on degree-lifted algebraic geometry codes

Revisions: 1

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TR12-102
| 16th August 2012
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Swastik Kopparty, Srikanth Srinivasan#### Certifying Polynomials for $\mathrm{AC}^0[\oplus]$ circuits, with applications

Swastik Kopparty, Noga Ron-Zewi, Shubhangi Saraf, Mary Wootters

In this work, we show new and improved error-correcting properties of folded Reed-Solomon codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the sources of recent advances in coding theory. Folded Reed-Solomon codes were the first explicit constructions ... more >>>

Eli Ben-Sasson, Swastik Kopparty, Shubhangi Saraf

Algebraic proof systems reduce computational problems to problems about estimating the distance of a sequence of functions $u=(u_1,\ldots, u_k)$, given as oracles, from a linear error correcting code $V$. The soundness of such systems relies on methods that act ``locally'' on $u$ and map it to a single function $u^*$ ... more >>>

Swastik Kopparty, Or Meir, Noga Ron-Zewi, Shubhangi Saraf

An error correcting code is said to be \emph{locally testable} if

there is a test that checks whether a given string is a codeword,

or rather far from the code, by reading only a small number of symbols

of the string. Locally testable codes (LTCs) are both interesting

in their ...
more >>>

Amey Bhangale, Swastik Kopparty, Sushant Sachdeva

Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design the first nontrivial approximation algorithms in this context.

Our main result is that ... more >>>

Eli Ben-Sasson, Yohay Kaplan, Swastik Kopparty, Or Meir, Henning Stichtenoth

The PCP theorem (Arora et. al., J. ACM 45(1,3)) says that every NP-proof can be encoded to another proof, namely, a probabilistically checkable proof (PCP), which can be tested by a verifier that queries only a small part of the PCP. A natural question is how large is the blow-up ... more >>>

Venkatesan Guruswami, Swastik Kopparty

A subspace design is a collection $\{H_1,H_2,\dots,H_M\}$ of subspaces of ${\mathbf F}_q^m$ with the property that no low-dimensional subspace $W$ of ${\mathbf F}_q^m$ intersects too many subspaces of the collection. Subspace designs were introduced by Guruswami and Xing (STOC 2013) who used them to give a randomized construction of optimal ... more >>>

Alan Guo, Swastik Kopparty, Madhu Sudan

In this work we explore error-correcting codes derived from

the ``lifting'' of ``affine-invariant'' codes.

Affine-invariant codes are simply linear codes whose coordinates

are a vector space over a field and which are invariant under

affine-transformations of the coordinate space. Lifting takes codes

defined over a vector space of small dimension ...
more >>>

Eli Ben-Sasson, Ariel Gabizon, Yohay Kaplan, Swastik Kopparty, Shubhangi Saraf

We describe new constructions of error correcting codes, obtained by "degree-lifting" a short algebraic geometry (AG) base-code of block-length $q$ to a lifted-code of block-length $q^m$, for arbitrary integer $m$. The construction generalizes the way degree-$d$, univariate polynomials evaluated over the $q$-element field (also known as Reed-Solomon codes) are "lifted" ... more >>>

Swastik Kopparty, Srikanth Srinivasan

In this paper, we introduce and develop the method of certifying polynomials for proving $\mathrm{AC}^0[\oplus]$ circuit lower bounds.

We use this method to show that Approximate Majority cannot be computed by $\mathrm{AC}^0[\oplus]$ circuits of size $n^{1+o(1)}$. This implies a separation between the power of $\mathrm{AC}^0[\oplus]$ circuits of near-linear size and ... more >>>