A systematic (16,8) code for correcting double errors and detecting triple-adjacent errors

A double error correcting systematic (16,8) quasi-cycle (QC) code that can detect all triple-adjacent errors within each 8-b byte is presented. This code is useful in computer memory applications where adjacent errors are more likely than random errors. As an alternative, a systematic (24,16) QC code is given which corrects single errors, and detects all double errors in addition to all triple-adjacent and quadruple-adjacent errors. A third code, a systematic (32,16) QC code, is presented which corrects all triple errors and detects all quadruple errors. Decoding can be achieved either by syndrome generation and table lookup or by majority logic