CS 559 : Algorithmic Aspects of Computer Networks Fall ’ 07 Lecture 2 — September 10 , 2007

the knowledge of any m independent equations (i.e. any m values of c, given that the corresponding m rows of A are independent) is enough to get bm. Without Loss of Generality (WLOG), we can divide the file F into columns of size m; bi where i = 1,2,...,L/m and apply the same transformation on them (i.e A), resulting in L/m columns of length n; cj where j =1,2,...,L/m. As illustrated in Figure 2.1. we call each row of C a dispersion and collecting any m dispersions would enable the user of retrieving F. More formally, let the retrieved pieces be C* and the corresponding rows of A be A*.