On the decoding of Preparata codes (Q1569279)

The author presents a decoding algorithm for extended Preparata codes that is similar to a decoding algorithm for BCH-codes described in an earlier paper (the author's reference [1]). He introduces a kind of syndrome (functions \(F_0\), \(F_0^*\), \(F_1\), \(F_3\) and \(F^*_3\)) based on which values he can distinguish between the cases of single, double, triple errors and compact byte errors (the last notion is not defined in the paper), and, in case of single, double errors and compact byte errors, the values of the syndrome can be used to locate the errors. The reader who wants to really understand the paper has to put a lot of effort in it since the material is not presented in a clear way. Especially, Lemma 1 requests a lot of goodwill from the side of the reader before it can be interpreted in the way it is meant (since underwater the equations containing \(k\) in the second line of the Lemma apparently are implicitly defining a dependence between \(k\) and \(i\), so in fact it would be much clearer if the author had used \(k_i\) instead of \(k\)). Nevertheless I think the paper is worth studying.