Some constructions of storage codes from grassmann graphs
Date of Issue2014
International Zurich Seminar on Communications (IZS), February 26–28, 2014
School of Physical and Mathematical Sciences
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.
© 2014 ETH-Zürich. This paper was published in International Zurich Seminar on Communications (IZS) and is made available as an electronic reprint (preprint) with permission of ETH-Zürich. The paper can be found at the following official DOI: [http://dx.doi.org/10.3929/ethz-a-010094830]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.