Alan Guo, Madhu Sudan

We prove that the class of locally testable affine-invariant properties is closed under sums, intersections and "lifts". The sum and intersection are two natural operations on linear spaces of functions, where the sum of two properties is simply their sum as a vector space. The "lift" is a less natural ... more >>>

Alan Guo, Madhu Sudan

In this work we explore error-correcting codes derived from

the ``lifting'' of ``affine-invariant'' codes.

Affine-invariant codes are simply linear codes whose coordinates

are a vector space over a field and which are invariant under

affine-transformations of the coordinate space. Lifting takes codes

defined over a vector space of small dimension ...
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Alan Guo, Swastik Kopparty, Madhu Sudan

the ``lifting'' of ``affine-invariant'' codes.

Affine-invariant codes are simply linear codes whose coordinates

are a vector space over a field and which are invariant under

affine-transformations of the coordinate space. Lifting takes codes

defined over a vector space of small dimension ...
more >>>

Elad Haramaty, Noga Ron-Zewi, Madhu Sudan

In this work we present a strong analysis of the testability of a broad, and to date the most interesting known, class of "affine-invariant'' codes. Affine-invariant codes are codes whose coordinates are associated with a vector space and are invariant under affine transformations of the coordinate space. Affine-invariant linear codes ... more >>>

Alan Guo, Elad Haramaty, Madhu Sudan

A local tester for a code probabilistically looks at a given word at a small set of coordinates and based on this local view accepts codewords with probability one while rejecting words far from the code with constant probabilility. A local tester for a code is said to be ``robust'' ... more >>>