23 citations · 98 across the 30 of their papers we have counts for
4 papers · 1 filter
High dimensional expansion implies amplified local testability
Tali Kaufman, Izhar Oppenheim
In this work we show that high dimensional expansion implies locally testable code. Specifically, we define a notion that we call high-dimensional-expanding-system (HDE-system). Th…
Edge Transitive Ramanujan Graphs and Highly Symmetric LDPC Good Codes
Tali Kaufman, Alexander Lubotzky
We present a symmetric LDPC code with constant rate and constant distance (i.e. good LDPC code) that its constraint space is generated by the orbit of one constant weight constrain…
Succinct Representation of Codes with Applications to Testing
Elena Grigorescu, Tali Kaufman, Madhu Sudan
Motivated by questions in property testing, we search for linear error-correcting codes that have the "single local orbit" property: i.e., they are specified by a single local cons…
The List-Decoding Size of Reed-Muller Codes
Tali Kaufman, Shachar Lovett
In this work we study the list-decoding size of Reed-Muller codes. Given a received word and a distance parameter, we are interested in bounding the size of the list of Reed-Muller…