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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: | 06 Oct 2025 12:47 |
| URI: | https://epub.uni-bayreuth.de/id/eprint/7405 |
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