Abstrakti
In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. It is also shown that, with high probability, a random matrix with a few extra columns guaranteeing the locality property is a generator matrix for a locally repairable code with a good minimum distance. The proof of the result provides a constructive method to find locally repairable codes. Finally, constructions of three infinite classes of optimal vector-linear locally repairable codes over a small alphabet independent of the code size are given.
| Alkuperäiskieli | Englanti |
|---|---|
| Sivut | 1129-1143 |
| Sivumäärä | 15 |
| Julkaisu | IEEE Transactions on Information Theory |
| Vuosikerta | 62 |
| Numero | 3 |
| DOI - pysyväislinkit | |
| Tila | Julkaistu - maalisk. 2016 |
| OKM-julkaisutyyppi | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä |
Rahoitus
This work was partially supported by the Academy of Finland under Grants 276031, 282938, and 283262, and by a grant from Magnus Ehrnrooth Foundation, Finland. The support from the European Science Foundation under the ESF COST Action IC1104 is also gratefully acknowledged. Preliminary results related to this work were reported at the 2014 Global Wireless Summit [1] and the 2014 IEEE Information Theory Workshop [2].