Abstract: Disclosed apparatus and method improve the computational efficiency of encoding and decoding data having erasures according to a maximum distance separable (MDS) code based on a Reed-Solomon code. Thus, n encoded fragments are formed by multiplying k data fragments by an n×k generator matrix for the MDS code. The code is formed by reducing, in the generator matrix to the extent possible, the size of the finite field to which entries belong—in some cases to the base field having only two elements. In this way, unlike codes known in the art, the generator matrix has more than one column whose entries each take values in the finite field having two elements. In some cases, the generator matrix has a column whose entries each take values in one or more intermediate fields between the finite field having two elements and the encoding field.

Abstract: Disclosed apparatus and method improve the computational efficiency of encoding and decoding data having erasures according to a maximum distance separable (MDS) code based on a Reed-Solomon code. Thus, n encoded fragments are formed by multiplying k data fragments by an n×k generator matrix for the MDS code. The code is formed by reducing, in the generator matrix to the extent possible, the size of the finite field to which entries belong—in some cases to the base field having only two elements. In this way, unlike codes known in the art, the generator matrix has more than one column whose entries each take values in the finite field having two elements. In some cases, the generator matrix has a column whose entries each take values in one or more intermediate fields between the finite field having two elements and the encoding field.