Finding good tree code constructions is among the most natural questions in error-correcting codes over the Hamming channel. Unlike the usual setting, where one encodes a single message against adversarial errors, tree codes allow a sender to encode and send a stream, in an online manner, while protecting it from ... more >>>

Residual-String Equality, denoted $\text{ResStringEq}$, is the property consisting of all pairs of strings over $\{0,1,*\}$ that are equal after deleting all `$*$' symbols from them. This property was first introduced by Fischer, Magniez, and Starikovskaya (SODA 2018), who used it to show a lower bound on testing the $\text{Dyck}$ languages, ... more >>>

Let $G=[n]$ and let an unknown binary operation $*:G\times G\to G$ be given by oracle access to its multiplication table. The tester is given $n$ explicitly as part of its input. A query chooses $x,y\in G$ and receives $x*y$. We study randomized adaptive two-sided property testers for deciding whether $(G,*)$ ... more >>>