On the Trustworthiness of Error-Correcting Codes

The use of error-correcting codes protects data against accidental or intentional errors, but to what extent can a decoded message be trusted? To answer this question, one has to take the role of the receiver. First, the maximum number of errors Lambda acceptable for decoding is fixed. With the weight distribution, the probability of false decoding can be calculated, conditioned on such a Lambda-bounded strategy. This probability is a monotonously increasing function in the channel error probability p and in the maximum number of accepted errors Lambda. Therefore, pure error detection is more trustworthy than error correction. Moreover, for sufficiently small p, codes with the lexicographically smallest weight distribution prove to be most trustworthy. An example of how to calculate and use the probability of false decoding is given in the context of the pseudonymization service of the German telematics platform TMF for health research networks.