Restricted isometry of Fourier matrices and list decodability of random linear codes
We prove that a random linear code over F_q, with probability arbitrarily close to 1, is list
decodable at radius 1-1/q-ϵ with list size L=O(1/ϵ^2) and rate R=\Omega_q(ϵ^2/(\log^3(1/ϵ …
decodable at radius 1-1/q-ϵ with list size L=O(1/ϵ^2) and rate R=\Omega_q(ϵ^2/(\log^3(1/ϵ …
Reed-Muller codes for random erasures and errors
This paper studies the parameters for which binary Reed-Muller (RM) codes can be
decoded successfully on the BEC and BSC, and in particular when can they achieve …
decoded successfully on the BEC and BSC, and in particular when can they achieve …
Testing Fourier dimensionality and sparsity
We present a range of new results for testing properties of Boolean functions that are
defined in terms of the Fourier spectrum. Broadly speaking, our results show that the …
defined in terms of the Fourier spectrum. Broadly speaking, our results show that the …
Weight distribution and list-decoding size of reed–muller codes
The weight distribution and list-decoding size of Reed-Muller codes are studied in this work.
Given a weight parameter, we are interested in bounding the number of Reed-Muller …
Given a weight parameter, we are interested in bounding the number of Reed-Muller …
Every list-decodable code for high noise has abundant near-optimal rate puncturings
We show that any q-ary code with sufficiently good distance can be randomly punctured to
obtain, with high probability, a code that is list decodable up to radius 1---1/q---ε with near …
obtain, with high probability, a code that is list decodable up to radius 1---1/q---ε with near …
Efficient algorithms for the bee-identification problem
The bee-identification problem, formally defined by Tandon, Tan, and Varshney (2019),
requires the receiver to identify “bees” using a set of unordered noisy measurements. In this …
requires the receiver to identify “bees” using a set of unordered noisy measurements. In this …
List decoding of binary codes–a brief survey of some recent results
V Guruswami - … and Cryptology: Second International Workshop, IWCC …, 2009 - Springer
We briefly survey some recent progress on list decoding algorithms for binary codes. The
results discussed include: Algorithms to list decode binary Reed-Muller codes of any order …
results discussed include: Algorithms to list decode binary Reed-Muller codes of any order …
Efficiently decoding Reed-Muller codes from random errors
Reed-Muller codes encode an m-variate polynomial of degree r by evaluating it on all points
in {0, 1} m. We denote this code by RM (m, r). The minimal distance of RM (m, r) is 2 m− r …
in {0, 1} m. We denote this code by RM (m, r). The minimal distance of RM (m, r) is 2 m− r …
On the list decodability of random linear codes with large error rates
M Wootters - Proceedings of the forty-fifth annual ACM symposium …, 2013 - dl.acm.org
It is well known that a random q-ary code of rate Ω (ε2) is list decodable up to radius (1-1/q-ε)
with list sizes on the order of 1/ε2, with probability 1-o (1). However, until recently, a similar …
with list sizes on the order of 1/ε2, with probability 1-o (1). However, until recently, a similar …
Improved list decoding of folded reed-solomon and multiplicity codes
We show new and improved list decoding properties of folded Reed–Solomon (RS) codes
and multiplicity codes. Both of these families of codes are based on polynomials over finite …
and multiplicity codes. Both of these families of codes are based on polynomials over finite …