Matches in SemOpenAlex for { <https://semopenalex.org/work/W4300641916> ?p ?o ?g. }
Showing items 1 to 76 of
76
with 100 items per page.
- W4300641916 abstract "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 relative distance, and query complexity $exp(tilde{O}(sqrt{log n}))$. Previously such codes were known to exist only with $Omega(n^{beta})$ query complexity (for constant $beta > 0$), and there were several, quite different, constructions known. Our codes are based on a general distance-amplification method of Alon and Luby~cite{AL96_codes}. We show that this method interacts well with local correctors and testers, and obtain our main results by applying it to suitably constructed LCCs and LTCs in the non-standard regime of emph{sub-constant relative distance}. Along the way, we also construct LCCs and LTCs over large alphabets, with the same query complexity $exp(tilde{O}(sqrt{log n}))$, which additionally have the property of approaching the Singleton bound: they have almost the best-possible relationship between their rate and distance. This has the surprising consequence that asking for a large alphabet error-correcting code to further be an LCC or LTC with $exp(tilde{O}(sqrt{log n}))$ query complexity does not require any sacrifice in terms of rate and distance! Such a result was previously not known for any $o(n)$ query complexity. Our results on LCCs also immediately give locally-decodable codes (LDCs) with the same parameters." @default.
- W4300641916 created "2022-10-03" @default.
- W4300641916 creator A5020540233 @default.
- W4300641916 creator A5031695135 @default.
- W4300641916 creator A5053736571 @default.
- W4300641916 creator A5071686980 @default.
- W4300641916 date "2015-04-22" @default.
- W4300641916 modified "2023-09-29" @default.
- W4300641916 title "High rate locally-correctable and locally-testable codes with sub-polynomial query complexity" @default.
- W4300641916 doi "https://doi.org/10.48550/arxiv.1504.05653" @default.
- W4300641916 hasPublicationYear "2015" @default.
- W4300641916 type Work @default.
- W4300641916 citedByCount "0" @default.
- W4300641916 crossrefType "posted-content" @default.
- W4300641916 hasAuthorship W4300641916A5020540233 @default.
- W4300641916 hasAuthorship W4300641916A5031695135 @default.
- W4300641916 hasAuthorship W4300641916A5053736571 @default.
- W4300641916 hasAuthorship W4300641916A5071686980 @default.
- W4300641916 hasBestOaLocation W43006419161 @default.
- W4300641916 hasConcept C112876837 @default.
- W4300641916 hasConcept C114614502 @default.
- W4300641916 hasConcept C118615104 @default.
- W4300641916 hasConcept C121332964 @default.
- W4300641916 hasConcept C134306372 @default.
- W4300641916 hasConcept C138885662 @default.
- W4300641916 hasConcept C177264268 @default.
- W4300641916 hasConcept C199360897 @default.
- W4300641916 hasConcept C2776760102 @default.
- W4300641916 hasConcept C2777027219 @default.
- W4300641916 hasConcept C2779557605 @default.
- W4300641916 hasConcept C33923547 @default.
- W4300641916 hasConcept C41008148 @default.
- W4300641916 hasConcept C41895202 @default.
- W4300641916 hasConcept C48372109 @default.
- W4300641916 hasConcept C62520636 @default.
- W4300641916 hasConcept C63553672 @default.
- W4300641916 hasConcept C77553402 @default.
- W4300641916 hasConcept C90119067 @default.
- W4300641916 hasConcept C94375191 @default.
- W4300641916 hasConceptScore W4300641916C112876837 @default.
- W4300641916 hasConceptScore W4300641916C114614502 @default.
- W4300641916 hasConceptScore W4300641916C118615104 @default.
- W4300641916 hasConceptScore W4300641916C121332964 @default.
- W4300641916 hasConceptScore W4300641916C134306372 @default.
- W4300641916 hasConceptScore W4300641916C138885662 @default.
- W4300641916 hasConceptScore W4300641916C177264268 @default.
- W4300641916 hasConceptScore W4300641916C199360897 @default.
- W4300641916 hasConceptScore W4300641916C2776760102 @default.
- W4300641916 hasConceptScore W4300641916C2777027219 @default.
- W4300641916 hasConceptScore W4300641916C2779557605 @default.
- W4300641916 hasConceptScore W4300641916C33923547 @default.
- W4300641916 hasConceptScore W4300641916C41008148 @default.
- W4300641916 hasConceptScore W4300641916C41895202 @default.
- W4300641916 hasConceptScore W4300641916C48372109 @default.
- W4300641916 hasConceptScore W4300641916C62520636 @default.
- W4300641916 hasConceptScore W4300641916C63553672 @default.
- W4300641916 hasConceptScore W4300641916C77553402 @default.
- W4300641916 hasConceptScore W4300641916C90119067 @default.
- W4300641916 hasConceptScore W4300641916C94375191 @default.
- W4300641916 hasLocation W43006419161 @default.
- W4300641916 hasLocation W43006419162 @default.
- W4300641916 hasOpenAccess W4300641916 @default.
- W4300641916 hasPrimaryLocation W43006419161 @default.
- W4300641916 hasRelatedWork W1673132890 @default.
- W4300641916 hasRelatedWork W1989417921 @default.
- W4300641916 hasRelatedWork W1997643965 @default.
- W4300641916 hasRelatedWork W2017783420 @default.
- W4300641916 hasRelatedWork W2067936666 @default.
- W4300641916 hasRelatedWork W2134460193 @default.
- W4300641916 hasRelatedWork W2216908642 @default.
- W4300641916 hasRelatedWork W3164081298 @default.
- W4300641916 hasRelatedWork W4296603869 @default.
- W4300641916 hasRelatedWork W2183411100 @default.
- W4300641916 isParatext "false" @default.
- W4300641916 isRetracted "false" @default.
- W4300641916 workType "article" @default.