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.

Let C be a linear [n,k,d]-code over GF(q) with k/spl ges/2. If s=n-k+1-d denotes the defect of C, then by the Griesmer bound, d/spl les/(s+1)q. Now, for obvious reasons, we are interested in codes of given defect s for which the minimum distance is maximal, i.e., d=(s+1)q. We classify up to formal equivalence all such linear codes over GF(q). Remember that two codes over GF(q) are formally equivalent if they have the same weight distribution. It turns out that for k/spl ges/3 such codes exist only in dimension 3 and 4 with the ternary extended Golay code, the ternary dual Golay code, and the binary even-weight code as exceptions. In dimension 4 they are related to ovoids in PG(3,q) except the binary extended Hamming code, and in dimension 3 to maximal arcs in PG(2,q).

Let C be an [n,k,d]-code over GP(q) with k/spl ges/2. Let s=def(C)=n+1-k-d denote the defect of C. The Griesmer bound implies that d/spl les/q(s+1). If d>qs and s/spl ges/2, then using a previous result of Faldum and Willems, k/spl les/q. Thus fixing s/spl ges/2 the extreme parameters for a code with def(C)=s are d=q(s+1); k=q, and n=k+d+s-1=(q+1)(s+2)-3. In this correspondence we characterize the codes with such parameters.