Recovery Sets for Subspaces from a Vector Space

摘要

Recovery sets for vectors and subspaces are important in constructions of distributed storage system codes. These concepts are also interesting in their own right. In this paper we consider the following very basic recovery question: what is the maximum number of possible pairwise disjoint recovery sets if the recovered element is a d-dimensional subspace and the elements stored are the one-dimensional subspaces of an n-dimensional vector space over GF(q). Lower and upper bounds on the number of such recovery sets are provided. It is shown that generally these bounds are either tight or very close of being tight.