2012/03/09 by Hongmei Xie, Zhiyuan Yan, Xie, Hongmei +1
Computer Science · Mathematics · #Advanced Data Storage Technologies #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1203.2202
This paper has been withdrawn by the author due to incorrect statements
openalex publication_date 2012/03/09 · arxiv created 2013/01/21 · arxiv updated 2013/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose two new constructions of exact-repair minimum storage regenerating (exact-MSR) codes. For both constructions, the encoded symbols are obtained by treating the message vector over GF(q) as a linearized polynomial and evaluating it over an extension field GF(qm). For our exact-MSR codes, data repair does not need matrix inversion, and can be implemented by additions and multiplications over GF(q) as well as cyclic shifts when a normal basis is used. The two constructions assume a base field of GF(q) (q>2) and GF(2), respectively. In contrast to existing constructions of exact-MSR codes, the former construction works for arbitrary code parameters, provided that q is large enough. This is the first construction of exact-MSR codes with arbitrary code parameters, to the best of our knowledge. In comparison to existing exact-MSR codes, while data construction of our exact-MSR codes has a higher complexity, the complexity of data repair is lower. Thus, they are attractive for applications that need a small number of data reconstructions along with a large number of data repairs.