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Bounds on the maximal minimum distance of linear locally repairable codes

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Pöllänen, Antti
dc.contributor.author Westerbäck, Thomas
dc.contributor.author Freij-Hollanti, Ragnar
dc.contributor.author Hollanti, Camilla
dc.date.accessioned 2017-08-03T12:09:41Z
dc.date.available 2017-08-03T12:09:41Z
dc.date.issued 2016-08-10
dc.identifier.citation Pöllänen , A , Westerbäck , T , Freij-Hollanti , R & Hollanti , C 2016 , Bounds on the maximal minimum distance of linear locally repairable codes . in Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory . vol. 2016-August , 7541566 , IEEE International Symposium on Information Theory , IEEE , pp. 1586-1590 , IEEE International Symposium on Information Theory , Barcelona , Spain , 10/07/2016 . https://doi.org/10.1109/ISIT.2016.7541566 en
dc.identifier.isbn 978-1-5090-1806-2
dc.identifier.issn 2157-8095
dc.identifier.issn 2157-8117
dc.identifier.other PURE UUID: 92dcdee0-1240-443c-bd1f-321cea1d5292
dc.identifier.other PURE ITEMURL: https://research.aalto.fi/en/publications/bounds-on-the-maximal-minimum-distance-of-linear-locally-repairable-codes(92dcdee0-1240-443c-bd1f-321cea1d5292).html
dc.identifier.other PURE LINK: http://www.scopus.com/inward/record.url?scp=84985914255&partnerID=8YFLogxK
dc.identifier.other PURE FILEURL: https://research.aalto.fi/files/14353489/Bounds_on_the_maximal_minimum_distance_of_linear_locally_repairable_codes.pdf
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/27399
dc.description.abstract Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication between storage nodes. There is a close connection between almost affine LRCs and matroid theory which can be utilized to construct good LRCs and derive bounds on their performance. A generalized Singleton bound for linear LRCs with parameters (n; k; d; r; δ) was given in [N. Prakash et al., 'Optimal Linear Codes with a Local-Error-Correction Property', IEEE Int. Symp. Inf. Theory]. In this paper, a LRC achieving this bound is called perfect. Results on the existence and nonexistence of linear perfect (n; k; d; r; δ)-LRCs were given in [W. Song et al., 'Optimal locally repairable codes', IEEE J. Sel. Areas Comm.]. Using matroid theory, these existence and nonexistence results were later strengthened in [T. Westerbäck et al., 'On the Combinatorics of Locally Repairable Codes', Arxiv: 1501.00153], which also provided a general lower bound on the maximal achievable minimum distance dmax(n; k; r; δ) that a linear LRC with parameters (n; k; r; δ) can have. This article expands the class of parameters (n; k; d; r; δ) for which there exist perfect linear LRCs and improves the lower bound for dmax(n; k; r; δ). Further, this bound is proved to be optimal for the class of matroids that is used to derive the existence bounds of linear LRCs. en
dc.format.extent 5
dc.format.extent 1586-1590
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher IEEE
dc.relation.ispartof IEEE International Symposium on Information Theory en
dc.relation.ispartofseries Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory en
dc.relation.ispartofseries Volume 2016-August en
dc.relation.ispartofseries IEEE International Symposium on Information Theory en
dc.rights openAccess en
dc.subject.other Theoretical Computer Science en
dc.subject.other Information Systems en
dc.subject.other Modelling and Simulation en
dc.subject.other Applied Mathematics en
dc.subject.other 113 Computer and information sciences en
dc.subject.other 111 Mathematics en
dc.title Bounds on the maximal minimum distance of linear locally repairable codes en
dc.type A4 Artikkeli konferenssijulkaisussa fi
dc.description.version Peer reviewed en
dc.contributor.department Department of Mathematics and Systems Analysis
dc.contributor.department Department of Communications and Networking
dc.subject.keyword Theoretical Computer Science
dc.subject.keyword Information Systems
dc.subject.keyword Modelling and Simulation
dc.subject.keyword Applied Mathematics
dc.subject.keyword 113 Computer and information sciences
dc.subject.keyword 111 Mathematics
dc.identifier.urn URN:NBN:fi:aalto-201708036367
dc.identifier.doi 10.1109/ISIT.2016.7541566
dc.type.version acceptedVersion


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