FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3201915762> ?p ?o ?g. }

• W3201915762 abstract "Lifted Reed-Solomon and multiplicity codes are classes of codes, constructed from specific sets of $m$-variate polynomials. These codes allow for the design of high-rate codes that can recover every codeword or information symbol from many disjoint sets. Recently, the underlying approaches have been combined for the bi-variate case to construct lifted multiplicity codes, a generalization of lifted codes that can offer further rate improvements. We continue the study of these codes by first establishing new lower bounds on the rate of lifted Reed-Solomon codes for any number of variables $m$, which improve upon the known bounds for any $mge 4$. Next, we use these results to provide lower bounds on the rate and distance of lifted multiplicity codes obtained from polynomials in an arbitrary number of variables, which improve upon the known results for any $mge 3$. Specifically, we investigate a subcode of a lifted multiplicity code formed by the linear span of $m$-variate monomials whose restriction to an arbitrary line in $mathbb{F}_q^m$ is equivalent to a low-degree univariate polynomial. We find the tight asymptotic behavior of the fraction of such monomials when the number of variables $m$ is fixed and the alphabet size $q=2^ell$ is large. Using these results, we give a new explicit construction of batch codes utilizing lifted Reed-Solomon codes. For some parameter regimes, these codes have a better trade-off between parameters than previously known batch codes. Further, we show that lifted multiplicity codes have a better trade-off between redundancy and the number of disjoint recovering sets for every codeword or information symbol than previously known constructions, thereby providing the best known PIR codes for some parameter regimes. Additionally, we present a new local self-correction algorithm for lifted multiplicity codes." @default.
• W3201915762 created "2021-10-11" @default.
• W3201915762 creator A5011128858 @default.
• W3201915762 creator A5021586372 @default.
• W3201915762 creator A5041582960 @default.
• W3201915762 creator A5079207347 @default.
• W3201915762 creator A5088225686 @default.
• W3201915762 date "2021-10-05" @default.
• W3201915762 modified "2023-09-27" @default.
• W3201915762 title "Lifted Reed-Solomon Codes and Lifted Multiplicity Codes." @default.
• W3201915762 cites W1505096007 @default.
• W3201915762 cites W1534925464 @default.
• W3201915762 cites W1941604706 @default.
• W3201915762 cites W1967703498 @default.
• W3201915762 cites W1968245619 @default.
• W3201915762 cites W1993830711 @default.
• W3201915762 cites W1996042140 @default.
• W3201915762 cites W2001766583 @default.
• W3201915762 cites W2018925011 @default.
• W3201915762 cites W2044199052 @default.
• W3201915762 cites W2048651540 @default.
• W3201915762 cites W2070864561 @default.
• W3201915762 cites W2088336724 @default.
• W3201915762 cites W2110354774 @default.
• W3201915762 cites W2113719649 @default.
• W3201915762 cites W2121417875 @default.
• W3201915762 cites W2125293366 @default.
• W3201915762 cites W2144581009 @default.
• W3201915762 cites W2146453677 @default.
• W3201915762 cites W2150616341 @default.
• W3201915762 cites W2345761008 @default.
• W3201915762 cites W2551008982 @default.
• W3201915762 cites W2557531834 @default.
• W3201915762 cites W2591083178 @default.
• W3201915762 cites W2610313478 @default.
• W3201915762 cites W2617207196 @default.
• W3201915762 cites W2751263082 @default.
• W3201915762 cites W2784847383 @default.
• W3201915762 cites W2811174140 @default.
• W3201915762 cites W2964263440 @default.
• W3201915762 cites W2989903737 @default.
• W3201915762 cites W3008928967 @default.
• W3201915762 cites W3047256406 @default.
• W3201915762 cites W3081428251 @default.
• W3201915762 cites W3167315446 @default.
• W3201915762 cites W3170752111 @default.
• W3201915762 cites W3197049764 @default.
• W3201915762 cites W411845244 @default.
• W3201915762 hasPublicationYear "2021" @default.
• W3201915762 type Work @default.
• W3201915762 sameAs 3201915762 @default.
• W3201915762 citedByCount "0" @default.
• W3201915762 crossrefType "posted-content" @default.
• W3201915762 hasAuthorship W3201915762A5011128858 @default.
• W3201915762 hasAuthorship W3201915762A5021586372 @default.
• W3201915762 hasAuthorship W3201915762A5041582960 @default.
• W3201915762 hasAuthorship W3201915762A5079207347 @default.
• W3201915762 hasAuthorship W3201915762A5088225686 @default.
• W3201915762 hasConcept C108509264 @default.
• W3201915762 hasConcept C11252640 @default.
• W3201915762 hasConcept C11413529 @default.
• W3201915762 hasConcept C114614502 @default.
• W3201915762 hasConcept C118615104 @default.
• W3201915762 hasConcept C121332964 @default.
• W3201915762 hasConcept C134306372 @default.
• W3201915762 hasConcept C153207627 @default.
• W3201915762 hasConcept C156004811 @default.
• W3201915762 hasConcept C157125643 @default.
• W3201915762 hasConcept C169021753 @default.
• W3201915762 hasConcept C2400350 @default.
• W3201915762 hasConcept C24890656 @default.
• W3201915762 hasConcept C2775997480 @default.
• W3201915762 hasConcept C33923547 @default.
• W3201915762 hasConcept C57273362 @default.
• W3201915762 hasConcept C78065487 @default.
• W3201915762 hasConceptScore W3201915762C108509264 @default.
• W3201915762 hasConceptScore W3201915762C11252640 @default.
• W3201915762 hasConceptScore W3201915762C11413529 @default.
• W3201915762 hasConceptScore W3201915762C114614502 @default.
• W3201915762 hasConceptScore W3201915762C118615104 @default.
• W3201915762 hasConceptScore W3201915762C121332964 @default.
• W3201915762 hasConceptScore W3201915762C134306372 @default.
• W3201915762 hasConceptScore W3201915762C153207627 @default.
• W3201915762 hasConceptScore W3201915762C156004811 @default.
• W3201915762 hasConceptScore W3201915762C157125643 @default.
• W3201915762 hasConceptScore W3201915762C169021753 @default.
• W3201915762 hasConceptScore W3201915762C2400350 @default.
• W3201915762 hasConceptScore W3201915762C24890656 @default.
• W3201915762 hasConceptScore W3201915762C2775997480 @default.
• W3201915762 hasConceptScore W3201915762C33923547 @default.
• W3201915762 hasConceptScore W3201915762C57273362 @default.
• W3201915762 hasConceptScore W3201915762C78065487 @default.
• W3201915762 hasLocation W32019157621 @default.
• W3201915762 hasOpenAccess W3201915762 @default.
• W3201915762 hasPrimaryLocation W32019157621 @default.
• W3201915762 hasRelatedWork W1482764555 @default.
• W3201915762 hasRelatedWork W1543977106 @default.
• W3201915762 hasRelatedWork W1545614041 @default.
• W3201915762 hasRelatedWork W1967141831 @default.
• W3201915762 hasRelatedWork W2003708786 @default.

• next