Summary
The 2018 International Symposium on Information Theory and Its Applications (ISITA2018)
2018
Session Number:We-AM-Poster
Session:
Number:We-AM-Poster.19
A New Bound of (r,δ)-Locally Repairable Codes over Finite Field of Small Order
Tomoya Hamada, Hideki Yagi,
pp.509-509
Publication Date:2018/10/18
Online ISSN:2188-5079
DOI:10.34385/proc.55.We-AM-Poster.19
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Summary:
Codes with locality (r; δ) introduced in [1] are called locally repairable codes (LRCs). The codes can repair δ- 1 erased symbols from at most other available r symbols locally, using the local-error correction property of a punctured code with minimum distance at least δ. In [1], an upper bound on the minimum distance was also given by generalizing the Singleton bound. Taking account of the order q of a finite field, Cadambe and Mazumdar [2] gave an upper bound on the dimension of LRCs for δ= 2, based on classical upper bounds for algebraic codes, which is called the C-M bound. For an arbitrary δ, a bound of LRCs depending on the order q was given in [3], which is based on the convexity of classical upper bounds. This bound is explicit but usually weaker than the C-M bound for large q and δ= 2. In this paper, we derived a C-M type bound of LRCs with locality (r;δ) based on the techniques developed in [2] and [3]. The derived bound is tighter than the bound in [3] for some parameters.