On neighbor distances and symmetry in group codes (Corresp.)
David Slepian · IEEE Transactions on Information Theory · 1971
This correspondence provides counterexamples to two frequently proposed conjectures concerning group codes for the Gaussian channel. It is shown 1) that a code for which the list of distances from codewordito all other words is independent ofiis not necessarily a group code, and 2) a group code ofMwords need not possess a transitive symmetry group of orderM.