Fractional decoding of r-Hermitian codes

Simple item page
dc.contributor.authorMatthews, Gretchen L.en
dc.contributor.authorMurphy, Aidan W.en
dc.contributor.authorSantos, Welingtonen
dc.date.accessioned2024-01-22T18:14:37Zen
dc.date.available2024-01-22T18:14:37Zen
dc.date.issued2023-12en
dc.description.abstractIn this paper, we present a fractional decoding algorithm for a new family of codes which are constructed from the Hermitian curve, called r-Hermitian codes. These codes of length n are defined over an extension field Fq2l of Fq2 and the fractional decoding algorithms that we present are algorithms for error correction that use only αln symbols of a subfield of size q2 as input into the decoding algorithm, where α<1, meaning a fraction of the subsymbols that are typically utilized. We demonstrate that collaborative decoding of interleaved codes supports fractional decoding of the r-Hermitian codes, allowing for improved bounds on the fractional decoding radius.en
dc.description.versionAccepted versionen
dc.format.extent25 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifierARTN 102278 (Article number)en
dc.identifier.doihttps://doi.org/10.1016/j.ffa.2023.102278en
dc.identifier.eissn1090-2465en
dc.identifier.issn1071-5797en
dc.identifier.orcidMatthews, Gretchen [0000-0002-8977-8171]en
dc.identifier.urihttps://hdl.handle.net/10919/117553en
dc.identifier.volume92en
dc.language.isoenen
dc.publisherAcademic Press – Elsevieren
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectCollaborative decodingen
dc.subjectDistributed storage systemen
dc.subjectFractional decodingen
dc.subjectHermitian curveen
dc.subjectInterleaved codeen
dc.subjectReed-Solomon codeen
dc.titleFractional decoding of r-Hermitian codesen
dc.title.serialFinite Fields And Their Applicationsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/Scienceen
pubs.organisational-group/Virginia Tech/Science/Mathematicsen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Science/COS T&R Facultyen

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Fractional decoding of r-Hermitian code.pdf
Size:
287.93 KB
Format:
Adobe Portable Document Format
Description:
Accepted version
Download
License bundle
Now showing 1 - 1 of 1
Name:
license.txt
Size:
1.5 KB
Format:
Plain Text
Description:
Download

Collections

All Faculty Deposits
Scholarly Works, Mathematics