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Bounds on the minimum distance of locally recoverable codes

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00007405
URN to cite this document: urn:nbn:de:bvb:703-epub-7405-7

Title data

Kurz, Sascha:
Bounds on the minimum distance of locally recoverable codes.
Bayreuth , 2024 . - 23 S.

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Abstract

We consider locally recoverable codes (LRCs) and aim to determine the smallest possible length n=n_q(k,d,r) of a linear [n,k,d]_q-code with locality r. For k at most 7 we exactly determine all values of n_2(k,d,2) and for k at most 6 we exactly determine all values of n_2(k,d,1). For the ternary field we also state a few numerical results. As a general result we prove that n_q(k,d,r) equals the Griesmer bound if the minimum Hamming distance d is sufficiently large and all other parameters are fixed.

Further data

Item Type: Preprint, postprint
Keywords: linear codes; locally recoverable codes; data storage; bounds for parameters
Subject classification: Mathematics Subject Classification Code: 94B27 (94B05)
DDC Subjects: 000 Computer Science, information, general works > 004 Computer science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics
Faculties
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-7405-7
Date Deposited: 19 Jan 2024 10:55
Last Modified: 19 Jan 2024 10:55
URI: https://epub.uni-bayreuth.de/id/eprint/7405

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