An error correction coding is provided that generates P bits of check data from K M-bit words of payload data. The P bits of check data include an address field A, a bit error indicating field E and an auxiliary field P−(E+A). The address field encodes a set of error addresses which has a cardinality equal to the bit size K of the payload data and providing a one-to-one mapping between values of the address field and the locations of a single bit error within the payload data. The bit error indicating field indicates if a bit error is present. The auxiliary field is a minimum size bit vector such that together with the address field and the bit area indicating field it provides a checksum for a systematic code for the payload data with a minimum Hamming distance serving to provide either single error correction capability or single error correction and double error detection capability.