In coding theory the problem of decoding focuses on error vectors. In the simplest situation code words are $(0,1)$-vectors, as are the received messages and the error vectors. Comparison of a received word with the code words yields a set of error vectors. In deciding on the original code word, usually the one for which the error vector has minimum Hamming weight is chosen. This note is a continuation of a first investigation of error patterns. First we consider burstiness and distribution of error vectors without assuming cyclic conditions. Then we define some forms of perfectness of codes and pose the problem of finding semi-perfect codes. The results of a systematic search for small vector lengths are presented. Finally a link is laid between error vectors, graphs and balanced incomplete block designs.
|Publisher||Department of Applied Mathematics, University of Twente|