1. A tangible computer readable hardware storage device, tangibly embodying computer readable code for providing an error correction code and parity protection for a given group of bits, wherein the given group of the bits comprises a plurality of subgroups of the bits, the computer readable code, when executing in a computer system, performing the following: using a specified error correction code checkbits generator matrix P comprising a plurality of rows and a plurality of columns to provide an error correction code and parity bits, including using the specified error correction code checkbits generator matrix P to provide an error correction code (ECC) for the given group of bits; and using two of the columns of said error correction code checkbits generator matrix P to provide parity bits for parity protection across the subgroups of said given group of bits.