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New Optimal Cyclic Locally Recoverable Codes of Length $n=2(q+1)$.
- Source :
-
IEEE Transactions on Information Theory . Jan2020, Vol. 66 Issue 1, p233-239. 7p. - Publication Year :
- 2020
-
Abstract
- Locally recoverable codes are very important due to their applications in distributed storage systems. In this paper, by using cyclic codes, we construct two classes of optimal q-ary cyclic $(\text {r}, \delta _{1})$ locally recoverable codes with parameters $[2(\text {q}+1), 2(\text {q}+1)-2\delta _{1}, \delta _{1}+2]_{\text {q}}$ , where $q$ is an odd prime power and $\text {r}+\delta _{1}-1=\text {q}+1$ , and $(\text {r}, \delta _{2})$ locally recoverable codes with parameters $[2(\text {q}+1), 2(\text {q}+1)-4\delta _{2}+2, \delta _{2}+2]_{q}$ , where $\text {q}\geq 7$ is an odd prime power, $\text {q}\equiv 3~ (mod~ 4)$ and $r+\delta _{2}-1=\frac {\text {q}+1}{2}$. Compared with the known cyclic and constacyclic $(\text {r}, \delta)$ locally recoverable codes, our construction yields new optimal cyclic $(\text {r}, \delta)$ locally recoverable codes. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 66
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 140827707
- Full Text :
- https://doi.org/10.1109/TIT.2019.2942304