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On neighbor distances and symmetry in group codes (Corresp.)

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1 Author(s)

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 codeword i to all other words is independent of i is not necessarily a group code, and 2) a group code of M words need not possess a transitive symmetry group of order M .

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IEEE Transactions on Information Theory  (Volume:17 ,  Issue: 5 )