Abstract: An error correcting and detecting system using a parity check H-matrix divided into a plurality of block vectors each including four or three column vectors each having eight elements. In the H-matrix, (i) there are no all "0" vectors; (ii) all column vectors are different from each other; (iii) 8 column vectors each having only one "1" is included therein, (iv) each column vector has an odd number of "1's"; (v) the modulo-2 sum of any three column vectors within any block never equals any column vectors of the H-matrix; (vi) the modulo-2 sum of four column vectors within any block never equals an all "0" vector; and (vii) the modulo-2 sum of eight column vectors within any two blocks never equals an all "0" vector.