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An Integer Programming-Based Bound for Locally Repairable Codes.
- Source :
- IEEE Transactions on Information Theory; Oct2015, Vol. 61 Issue 10, p5280-5294, 15p
- Publication Year :
- 2015
-
Abstract
- The locally repairable code (LRC) studied in this paper is an [n,k] linear code of which the value at each coordinate can be recovered by a linear combination of at most r other coordinates. The central problem in this paper is to determine the largest possible minimum distance for LRCs. First, an integer programming-based upper bound is derived for any LRC. Then, by solving the programming problem under certain conditions, an explicit upper bound is obtained for LRCs with parameters n1>n2 , where n1 = \lceil ({n}/{r+1}) \rceil and n2 = n1 (r+1) - n . Finally, an explicit construction for LRCs attaining this upper bound is presented over the finite field \mathbb F2^{m} , where m\geq n1r . Based on these results, the largest possible minimum distance for all LRCs with r \le \sqrt n-1 has been definitely determined, which is of great significance in practical use. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 61
- Issue :
- 10
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 109456278
- Full Text :
- https://doi.org/10.1109/TIT.2015.2472515