基于相对广义Hamming重量研究分布式存储中的数据恢复和数据安全

近年来，分布式存储技术在国内外掀起了研究热潮，也成为国家发展规划中大数据研究的重要一环。然而目前分布式存储系统中，一般很少考虑客户的多样化需求，例如结点部份（删截）数据的快速恢复问题、数据恢复同数据安全的平衡问题、满足多解需求的编码构造问题、存储介质性质问题等等，也较难精确刻画满足上述需求的模型结构。这正是此次课题申请需要解决的关键问题。. 申请人将利用与合作者提出的相对广义Hamming 重量概念，对基于直接线性编码或网络线性编码的分布式存储编码模式，提出满足上述理论与应用多样化需求、适应性强的存储方案与理论依据。另外，相对广义Hamming 重量本身的研究还可以对通信代数编码一系列经典性质进行推广，从子码的角度更好地理解原码的构造。

In recent years, “Big Data” has become a new ubiquitous term. Big Data is transforming “science, engineering, medicine, healthcare, finance, business, and the society itself”. Distributed storage is obviously an important part of it. However, in distributed storage systems, one problem is that the reliability is often maintained using erasure coding, replication and regenerating code, which cannot be designed to meet multiple requirements such as partial recovery, trade-off between security and recovery, practical list decoding, and material performance. Recently, network coding techniques have been suggested in addressing these challenges, establishing that maintenance bandwidth can be reduced by orders of magnitude compared to standard erasure codes. In this proposal, we prefer Relative Generalized Hamming Weight to deal with the problem, which also works on network coding.. The dimension/length profile (DLP) and the generalized Hamming weight (GHW) hierarchy of a linear code play an important role in coding theory, especially in trellis complexity, secure communication, multiple access communication and puncturing codes. It is worth noting that trellis complexity has been applied to the satellite system of NASA. By investigating the wiretap channel of type II with illegitimate parties, Luo et.al introduced the relative generalized Hamming weight (RGHW) hierarchy of a linear code and a subcode, which is a generalization of GHW hierarchy. Some equivalent concepts are relative dimension/length profile (RDLP), inverse relative dimension/ length profile (IRDLP) and relative length/dimension profile (RLDP). Recently, Zhang et al. extended RGHW hierarchy to secure network coding and described the equivocation to an eavesdropper in the wiretap network II with side information leakage.. Here we study important properties (maybe asymptotical) of RGHW, its equivalent concepts, its coding constructions, and then apply them to the (full or partial) recovery ability of linear coding data storage system combining with data security. For achieving the multiple requirements, we focus on not only the coding rate, the data security, but also on various storage materials, practical list decoding and their realization.