Use of Gauss-Jordan matrix reduction in the reconstruction of a correct file copy from erroneous copies

We describe a scheme, based on Gauss-Jordan matrix reduction technique, for the efficient location of errors in multiple file copies in a distributed environment, given that all copies may be partially erroneous. The file is subdivided into pages. Each page is represented by a C-bit signature. The only checking memory retained for each file copy is a highly protected overall file signature of C bits, where C is of the order of about 40-100 bits, derived as the vector sum of page signatures. Disagreeing page signatures are found and their processing is used to determine the correct and erroneous pages at all sites. If there is at least one site that has a correct copy of each page, and the number of erroneous pages is somewhat less than C, the scheme will almost always succeed in reconstructing a correct copy with a polynomial growth of computation with the number of erroneous pages.<>