Metrics of error locating codes

Error locating codes were first presented by Wolf and Elspas (1963). Error locating codes suitable for byte-organized semiconductor memory systems have been proposed. It is apparent that the code conditions of error correcting/detecting codes are expressed by the Hamming distance, but, on the other hand, those of error locating codes cannot always be expressed by only the Hamming distance. That is, the algebraic structure of the error locating codes has not yet been clarified. This paper defines a new metric for the error locating codes and then deduces the necessary and sufficient conditions of the codes by using the metric. These conditions clarify the relation between the code functions of error location and error correction/detection