2012/03/23 by Hongmei Xie, Zhiyuan Yan, Xie, Hongmei +1
Computer Science · Mathematics · #Advanced Data Storage Technologies #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1203.5325
This paper has been withdrawn by the author due to incorrect statements
openalex publication_date 2012/03/23 · 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-MBR) codes. Both constructions obtain the encoded symbols by first treating the message vector over GF(q) as a linearized polynomial and then evaluating it over an extension field GF(qm). The evaluation points are chosen so that the encoded symbols at any node are conjugates of each other, while corresponding symbols of different nodes are linearly dependent with respect to GF(q). These properties ensure that data repair can be carried out over the base field GF(q), instead of matrix inversion over the extension field required by some existing exact-MBR codes. To the best of our knowledge, this approach is novel in the construction of exact-MBR codes. One of our constructions leads to exact-MBR codes with arbitrary parameters. These exact-MBR codes have higher data reconstruction complexities but lower data repair complexities than their counterparts based on the product-matrix approach; hence they may be suitable for applications that need a small number of data reconstructions but a large number of data repairs.