A q-locally correctable code (LCC) C:{0,1\}^k→{0,1\}^n is a code in which it is possible to
correct every bit of a (not too) corrupted codeword by making at most q queries to the word …

We give improved lower bounds for binary 3-query locally correctable codes (3-LCCs)
C:{\0,1\}^k→{\0,1\}^n. Specifically, we prove: 1) If C is a linear design 3-LCC, then n≧2^(1 …

Matrix concentration inequalities, intimately connected to the Non-Commutative Khintchine
inequality, have been an important tool in both applied and pure mathematics. We study …

Given a $ k $-uniform hypergraph $ H $ on $ n $ vertices, an even cover in $ H $ is a
collection of hyperedges that touch each vertex an even number of times. Even covers are a …

Locally decodable codes (LDC's) are error-correcting codes that allow recovery of individual
message indices by accessing only a constant number of codeword indices. For substitution …

Motivated by connections between algebraic complexity lower bounds and tensor
decompositions, we investigate Koszul-Young flattenings, which are the main ingredient in …

We prove that for every odd $ q\geq 3$, any $ q $-query binary, possibly non-linear locally
decodable code ($ q $-LDC) $ E:\{\pm1\}^ k\rightarrow\{\pm1\}^ n $ must satisfy $ k\leq\tilde …

We give improved lower bounds for binary $3 $-query locally correctable codes (3-LCCs) $
C\colon\{0, 1\}^ k\rightarrow\{0, 1\}^ n $. Specifically, we prove:(1) If $ C $ is a linear design 3 …

A code $ C\colon\{0, 1\}^ k\to\{0, 1\}^ n $ is a $ q $-query locally decodable code ($ q $-LDC)
if one can recover any chosen bit $ b_i $ of the message $ b\in\{0, 1\}^ k $ with good …

We present simple constructions of good approxi-mate locally decodable codes (ALDCs) in
the presence of a δ- fraction of errors for δ<1/2. In a standard locally decodable code …