7 papers · 1 filter
Unique Decoding of Reed-Solomon and Related Codes for Semi-Adversarial Errors
Joshua Brakensiek, Yeyuan Chen, Manik Dhar +1
Motivated by recent developments in coding theory, particular in list-decoding, we introduce a new error model which we call semi-adversarial errors. This error model bridges betwe…
Improved Constructions and Lower Bounds for Maximally Recoverable Grid Codes
Joshua Brakensiek, Manik Dhar, Sivakanth Gopi
In this paper, we continue the study of Maximally Recoverable (MR) Grid Codes initiated by Gopalan et al. [SODA 2017]. More precisely, we study codes over an grid topo…
From Random to Explicit via Subspace Designs With Applications to Local Properties and Matroids
Joshua Brakensiek, Yeyuan Chen, Manik Dhar +1
In coding theory, a common question is to understand the threshold rates of various local properties of codes, such as their list decodability and list recoverability. A recent wor…
Combinatorial Bounds for List Recovery via Discrete Brascamp--Lieb Inequalities
Joshua Brakensiek, Yeyuan Chen, Manik Dhar +1
In coding theory, the problem of list recovery asks one to find all codewords of a given code which such that at least fraction of the symbols of lie in some pre…
AG Codes Achieve List-decoding Capacity over Constant-sized Fields
Joshua Brakensiek, Manik Dhar, Sivakanth Gopi +1
The recently-emerging field of higher order MDS codes has sought to unify a number of concepts in coding theory. Such areas captured by higher order MDS codes include maximally rec…
Generalized GM-MDS: Polynomial Codes are Higher Order MDS
Joshua Brakensiek, Manik Dhar, Sivakanth Gopi
The GM-MDS theorem, conjectured by Dau-Song-Dong-Yuen and proved by Lovett and Yildiz-Hassibi, shows that the generator matrices of Reed-Solomon codes can attain every possible con…