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Constructions of Partial MDS Codes Over Small Fields.
- Source :
- IEEE Transactions on Information Theory; Jun2019, Vol. 65 Issue 6, p3692-3701, 10p
- Publication Year :
- 2019
-
Abstract
- Partial MDS (PMDS) codes are a class of erasure-correcting array codes that combine local correction of the rows with global correction of the array. An $\boldsymbol {m}\times \boldsymbol {n}$ array code is called an $(\boldsymbol {r};\boldsymbol {s})$ PMDS code if each row belongs to an ${[}\boldsymbol {n},\boldsymbol {n}-\boldsymbol {r}, \boldsymbol {r}+\textbf {1}{]}$ MDS code and the code can correct erasure patterns consisting of $\boldsymbol {r}$ erasures in each row together with $\boldsymbol {s}$ more erasures anywhere in the array. While a recent construction by Calis and Koyluoglu generates $(\boldsymbol {r};\boldsymbol {s})$ PMDS codes for all $\boldsymbol {r}$ and $\boldsymbol {s}$ , its field size is exponentially large. In this paper, a family of PMDS codes with field size ${\mathcal{ O}}\left ({\max \{\boldsymbol {m},\boldsymbol {n}^{\boldsymbol {r}+\boldsymbol {s}}\}^{\boldsymbol {s}} }\right)$ is presented for the case where $\boldsymbol {r}= {\mathcal{ O}}(1), \boldsymbol {s}= {\mathcal{ O}}(1)$. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 65
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 136543509
- Full Text :
- https://doi.org/10.1109/TIT.2018.2890201