We propose a framework to study the effect of local recovery requirements of codeword symbols on the dimension of linear codes, based on a combinatorial proxy that we call "visible rank." The locality constraints of a linear code are stipulated by a matrix $H$ of $\star$'s and $0$'s (which we ... more >>>

We consider the proximity testing problem for error-correcting codes which consist in evaluations of multivariate polynomials either of bounded individual degree or bounded total degree. Namely, given an
oracle function $f : L^m \rightarrow \mathbb F_q$, where $L\subset \mathbb F_q$, a verifier distinguishes whether $f$ is the evaluation of a ... more >>>

At ITCS 2010, Dziembowski, Pietrzak, and Wichs introduced Non-malleable Codes (NMCs). Non-malleability is one of the strongest and most challenging notions of security considered in cryptography and protects against tampering attacks. In the context of coding schemes, non-malleability requires that it be infeasible to tamper the codeword of a message ... more >>>