12 citations · 27 across the 28 of their papers we have counts for
10 papers · 1 filter
Algebraic Expander Codes
Swastik Kopparty, Itzhak Tamo
Expander (Tanner) codes combine sparse graphs with local constraints, enabling linear-time decoding and asymptotically good distance--rate tradeoffs. A standard constraint-counting…
Fourier Sparsity of Delta Functions and Matching Vector PIRs
Fatemeh Ghasemi, Swastik Kopparty
In this paper we study a basic and natural question about Fourier analysis of Boolean functions, which has applications to the study of Matching Vector based Private Information Re…
High Rate Multivariate Polynomial Evaluation Codes
Swastik Kopparty, Mrinal Kumar, Harry Sha
The classical Reed-Muller codes over a finite field are based on evaluations of -variate polynomials of degree at most over a product set , for some …
Error-Correcting Graph Codes
Swastik Kopparty, Aditya Potukuchi, Harry Sha
In this paper, we construct Error-Correcting Graph Codes. An error-correcting graph code of distance is a family of graphs on a common vertex set of size , such that if…
Improved decoding of Folded Reed-Solomon and Multiplicity Codes
Swastik Kopparty, Noga Ron-Zewi, Shubhangi Saraf +1
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 ove…
Syndrome decoding of Reed-Muller codes and tensor decomposition over finite fields
Swastik Kopparty, Aditya Potukuchi
Reed-Muller codes are some of the oldest and most widely studied error-correcting codes, of interest for both their algebraic structure as well as their many algorithmic properties…