All reports by Author Alan Guo:

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TR15-043
| 2nd April 2015
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Alan Guo, Elad Haramaty, Madhu Sudan#### Robust testing of lifted codes with applications to low-degree testing

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TR13-053
| 4th April 2013
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Alan Guo#### High rate locally correctable codes via lifting

Revisions: 1

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TR12-149
| 8th November 2012
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Alan Guo, Swastik Kopparty, Madhu Sudan#### New affine-invariant codes from lifting

Comments: 1

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TR12-106
| 27th August 2012
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Alan Guo, Madhu Sudan#### New affine-invariant codes from lifting

Comments: 1

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TR12-048
| 25th April 2012
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Alan Guo, Madhu Sudan#### Some closure features of locally testable affine-invariant properties

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 >>>

Alan Guo

We present a general framework for constructing high rate error correcting codes that are locally correctable (and hence locally decodable if linear) with a sublinear number of queries, based on lifting codes with respect to functions on the coordinates. Our approach generalizes the lifting of affine-invariant codes of Guo, Kopparty, ... more >>>

Alan Guo, Swastik Kopparty, 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 ...
more >>>

Alan Guo, 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 >>>

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 >>>