33 citations · 74 across the 23 of their papers we have counts for
32 papers
Reed-Solomon Codes at Capacity: Algorithmic List-Decoding and Proximity Gaps
Prahladh Harsha, Mrinal Kumar, Ramprasad Saptharishi
Understanding the limits of list-decodability of Reed-Solomon codes has been one of the most important open problems in algebraic coding theory. Recently, Brakensiek, Chen, Putterm…
Hitting Sets for Polynomials with Small Partial Derivative Spaces
Shubham Bhardwaj, Ramprasad Saptharishi
We give an explicit hitting set of size for the class of -variate degree- polynomials whose partial derivative space is bounded by , over any field $\…
Constant-depth circuits for polynomial GCD over any characteristic
Somnath Bhattacharjee, Mrinal Kumar, Shanthanu Rai +3
We show that the GCD of two univariate polynomials can be computed by (piece-wise) algebraic circuits of constant depth and polynomial size over any sufficiently large field, regar…
Closure under factorization from a result of Furstenberg
Somnath Bhattacharjee, Mrinal Kumar, Shanthanu S. Rai +3
We show that algebraic formulas and constant-depth circuits are closed under taking factors. In other words, we show that if a multivariate polynomial over a field of characteristi…
Deterministic factorization of constant-depth algebraic circuits in subexponential time
Somnath Bhattacharjee, Mrinal Kumar, Varun Ramanathan +2
While efficient randomized algorithms for factorization of polynomials given by algebraic circuits have been known for decades, obtaining an even slightly non-trivial deterministic…
An exposition of recent list-size bounds of FRS Codes
Abhibhav Garg, Prahladh Harsha, Mrinal Kumar +2
In the last year, there have been some remarkable improvements in the combinatorial list-size bounds of Folded Reed Solomon codes and multiplicity codes. Starting from the work on…