9 problems

The paper constructs an explicit family of $2$-query locally testable codes with linear distance. Constant-rate conjecture. For an appropriate choice of parameters, this family has…

Parallel LTC amplification conjecture. There exists such a family for which the construction gives a parallel variant of the theorem on LTC amplification:

Conjecture. With an appropriate choice of local product codes, these complexes yield good locally testable codes (LTCs). Tensor products of projective Reed–Solomon codes are sugges…

A quantum locally testable code is a quantum error-correcting code whose validity can be tested through local checks. Quantum-LTC conjecture. High-dimensional expansion will be a k…

A locally testable code (LTC) is an error-correcting code for which membership can be tested by querying only a small number of coordinates. A genuine high-dimensional expander is…

Locally testable codes (LTCs) are error-correcting codes whose membership can be tested by inspecting only a small number of coordinates; a code has high rate when its rate is boun…

Let $X$ be a sheaved high-dimensional expander and let the modification process alter its sheaf by successively eliminating excess cohomology classes. Say that the process terminat…

Let a collection of linear codes be called product-expanding when the associated product code has the product-expansion property used in the paper. The product-expansion conjecture…

Let $\mathcal{A}$ and $\mathcal{B}$ be the classical codes used in the lifted product construction over a group $G$, and let $\mathcal{A}\otimes_G\mathcal{B}$ denote their lifted p…