## Title data

Kurz, Sascha:

**Bounds on the minimum distance of locally recoverable codes.**

Bayreuth
,
2024
. - 23 p.

DOI: https://doi.org/10.15495/EPub_UBT_00007405

## Abstract in another language

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) |

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 |

Result of work at the UBT: | Yes |

DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |

Date Deposited: | 20 Jan 2024 22:05 |

Last Modified: | 22 Jan 2024 07:12 |

URI: | https://eref.uni-bayreuth.de/id/eprint/88307 |