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REPORTS > KEYWORD > LIFTING:
Reports tagged with Lifting:
TR12-106 | 27th August 2012
Alan Guo, Madhu Sudan

New affine-invariant codes from lifting

Comments: 1

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 >>>


TR12-149 | 8th November 2012
Alan Guo, Swastik Kopparty, Madhu Sudan

New affine-invariant codes from lifting

Comments: 1

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 >>>


TR13-030 | 20th February 2013
Elad Haramaty, Noga Ron-Zewi, Madhu Sudan

Absolutely Sound Testing of Lifted Codes

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 >>>


TR13-053 | 4th April 2013
Alan Guo

High rate locally correctable codes via lifting

Revisions: 1

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 >>>


TR17-029 | 18th February 2017
Clement Canonne, Tom Gur

An Adaptivity Hierarchy Theorem for Property Testing

Revisions: 1

Adaptivity is known to play a crucial role in property testing. In particular, there exist properties for which there is an exponential gap between the power of \emph{adaptive} testing algorithms, wherein each query may be determined by the answers received to prior queries, and their \emph{non-adaptive} counterparts, in which all ... more >>>


TR19-103 | 7th August 2019
Arkadev Chattopadhyay, Yuval Filmus, Sajin Koroth, Or Meir, Toniann Pitassi

Query-to-Communication Lifting Using Low-Discrepancy Gadgets

Lifting theorems are theorems that relate the query complexity of a function $f:\left\{ 0,1 \right\}^n\to \left\{ 0,1 \right\}$ to the communication complexity of the composed function $f\circ g^n$, for some “gadget” $g:\left\{ 0,1 \right\}^b\times \left\{ 0,1 \right\}^b\to \left\{ 0,1 \right\}$. Such theorems allow transferring lower bounds from query complexity to ... more >>>




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