Codes on Matrices and Some Applications

In many scenarios, there is a need to design error correcting codes that are required to correct erasures of certain types, unlike the random erasures observed at the output of a binary erasure channel. This has led us to study codes based on matrices.In this case, the code is described by a collection of matrices where the distance between two matrices is defined suitably so that certain type of erasure patterns can be corrected. For example, suppose a matrix is chosen from this collection and the entries in the first two rows and the first two columns of this matrix are erased. Can we still recover the original matrix? In this paper, we study such codes. The application of these codes to distributed storage is described.