Some Constructions of Storage Codes from Grassmann Graphs
Frédérique Oggier · DR-NTU (Nanyang Technological University) · 2014
Codes for distributed storage systems may be seen as families of m-dimensional subspaces of the vector space Fnq, where Fq is the finite field with q elements, q a prime power. These subspaces need to intersect, to allow (collaborative) repair. We consider the Grassmann graph Gq(n, m) which has for vertex set the collection of m-dimensional subspaces of Fnq, and two vertices are adjacent whenever they intersect in a hyperplane. To obtain subspaces with regular intersection pattern, we look for cliques in the Grassmann graph, and obtain preliminary examples of storage codes, whose parameters we study, in terms of storage overhead, and repairability.