ON THE CONSTRUCTION OF GROUP BLOCK-CODES

We consider the construction of group block codes, i.e., subgroups of G(n), the n-fold direct product of a group G. Two concepts are introdu ced that make this construction similar to that of codes over GF(2). T he first concept is that of an indecomposable code. The second is that of a parity-check matrix. As a result, group block codes over- a deco mposable Abelian group of exponent d(m) can be seen as block codes ove r the ring of residues module d,, and their minimum Hamming distance c an be easily determined. We also prove that, under certain technical c onditions, (n, k) systematic group block codes over non-Abelian groups are asymptotically bad, in the sense that their minimum Hamming dista nce cannot exceed [n/k].