Patent ID: 7581156

Claim:
A method for efficient transmission of a data field when, prior to transmission, the data field includes a number of failures less than or equal to three, comprising: generating by at least one computer processor data representing a Vandermonde matrix over GF(2 n ) by: generating an identity matrix portion; generating an erasure coding portion comprising data values corresponding to a set of three rows having a property that each minor of the set of three rows is invertible; and computing a determinant of a submatrix of the erasure coding portion, wherein said computing includes ignoring columns from the identity matrix portion, wherein said computing results in one of a 0 by 0, 1 by 1, 2 by 2 and 3 by 3 minor of the erasure coding portion remaining; using by the at least one computer processor the generated data representing the Vandermonde matrix to correct the failures in the data field; and in response to correcting the failures in the data field, transmitting by the at least one computer processor the data field to a recipient, the transmitting being made more efficient by correcting the failures in the data field prior to performing the transmitting.