A local tester for an error-correcting code is a probabilistic procedure that queries a small subset of coordinates, accepts codewords with probability one, and rejects non-codewords with probability proportional to their distance from the code. The local tester is {\em robust} if for non-codewords it satisfies the stronger property that ... more >>>
A locally testable code (LTC) is an error correcting code that has a property-tester. The tester reads $q$ bits that are randomly chosen, and rejects words with probability proportional to their distance from the code. The parameter $q$ is called the locality of the tester.
LTCs were initially studied as ... more >>>
This text provides a high-level description of the locally testable code constructed by Dinur, Evra, Livne, Lubotzky, and Mozes (ECCC, TR21-151).
In particular, the group theoretic aspects are abstracted as much as possible.
We give new bounds on the cosystolic expansion constants of several families of high dimensional expanders, and the known coboundary expansion constants of order complexes of homogeneous geometric lattices, including the spherical building of $SL_n(F_q)$. The improvement applies to the high dimensional expanders constructed by Lubotzky, Samuels and Vishne, and ... more >>>
Tree codes, introduced in the seminal works of Schulman (STOC 93', IEEE Transactions on Information Theory 96') are codes designed for interactive communication. Encoding in a tree code is done in an online manner: the $i$-th codeword symbol depends only on the first $i$ message symbols. Codewords should have good ... more >>>
