Consider a linear [n, k, d] q code C. We say that the i th coordinate of C has locality r, if the
value at this coordinate can be recovered from accessing some other r coordinates of C …

This is a survey of pseudorandomness, the theory of efficiently generating objects that" look
random" despite being constructed using little or no randomness. This theory has …

Locally decodable codes are a class of" error-correcting codes." Error-correcting codes help
to ensure reliability when transmitting information over noisy channels. They allow a sender …

Interactive oracle proofs (IOPs) are a hybrid between interactive proofs and PCPs. In an IOP,
the prover is allowed to interact with a verifier (like in an interactive proof) by sending …

Locally correctable codes (LCCs) and locally testable codes (LTCs) are error-correcting
codes that admit local algorithms for correction and detection of errors. Those algorithms are …

In this work we explore error-correcting codes derived from the" lifting" of" affine-invariant"
codes. Affine-invariant codes are simply linear codes whose coordinates are a vector space …

A locally repairable code (LRC) is a linear code such that every code symbol can be
recovered by accessing a small number of other code symbols. In this paper, we study …

How complex is a given multivariate polynomial? The main point of this survey is that one
can learn a great deal about the structure and complexity of polynomials by studying (some …

An (r,δ,ϵ)-locally decodable code encodes ak-bit message x to an N-bit codeword C(x),
such that for every i∈k, the i th message bit can be recovered with probability 1-ϵ, by a …

We study the list-decodability of multiplicity codes. These codes, which are based on
evaluations of high-degree polynomials and their derivatives, have rate approaching 1 while …