Determination of best shortened linear codes

The quality of a block code is determined by its capability to protect data against undetectable errors and by the number of check bits that are required for that purpose. For a given number of check bits there are codes with optimum bit error detecting capability in shortened block lengths. These codes are determined and tabulated. The residual error characteristics of some of the tabulated codes are compared with those specified in ISO/CCITT or IEC standard data transmission protocols. For block lengths and bit error rates that are typical in process control applications, the residual error rate of the determined codes is more than six orders of magnitude smaller than that of codes specified by widely used standard transmission protocols.