Abstract: An S8ED system is implemented in a memory system to detect single errors involving one or more bits in a byte of subject data, stored in and retrieved from the memory system. Relationships between the subject data and parity data, which are used to detect errors in the subject data, are defined by a novel check matrix. The novel check matrix includes a number of constituent matrices, each of which includes eight (8) vectors. Each vector of a constituent matrix (i) has a number of elements which is equal to the number of parity bits used to detect errors in the subject data; (ii) is a concatenation of a building block vector, one or more instances of one of two base generating vectors, and one or more instances of the other of the two base generating vectors; and (iii) is distinct from all other vectors of the same constituent matrix.