Varshamov-Gilbert bounds for generalized concatenated codes in Euclidean space

Abstract

The author suggests the Varshamov-Gilbert bound as a method for evaluating and comparing various possible inner codes. The advantage is that in this way an evaluation can be obtained which is more or less neutral as far as the choice of outer code is concerned. A few examples are evaluated. It is concluded that set partitioning and generalized concatenation provide excellent possibilities for constructing codes for non-Hamming metrics. In the case of Euclidean spaces the appropriate dimension for the inner code seems to be >