  Generalized Product (GPC) Codes, an unification of Product Codes and
Integrated Interleaved (II) Codes, are presented. Applications for approaches
requiring local and global parities are described. The more general problem of
extending product codes by adding global parities is studied and an upper bound
on the minimum distance of such codes is obtained. Codes with one, two and
three global parities whose minimum distances meet the bound are presented.
Tradeoffs between optimality and field size are discussed.
