Swastik Kopparty, Noga Ron-Zewi, Shubhangi Saraf

In this work, we construct the first locally-correctable codes (LCCs), and locally-testable codes (LTCs) with constant rate, constant relative distance, and sub-polynomial query complexity. Specifically, we show that there exist binary LCCs and LTCs with block length $n$, constant rate (which can even be taken arbitrarily close to 1), constant ... more >>>

Swastik Kopparty, Or Meir, Noga Ron-Zewi, Shubhangi Saraf

An error correcting code is said to be \emph{locally testable} if

there is a test that checks whether a given string is a codeword,

or rather far from the code, by reading only a small number of symbols

of the string. Locally testable codes (LTCs) are both interesting

in their ...
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Omar Alrabiah, Venkatesan Guruswami, Ray Li

A simple, recently observed generalization of the classical Singleton bound to list-decoding asserts that rate $R$ codes are not list-decodable using list-size $L$ beyond an error fraction $\frac{L}{L+1} (1-R)$ (the Singleton bound being the case of $L=1$, i.e., unique decoding). We prove that in order to approach this bound for ... more >>>