Abstract
We consider codes C for which the decoding regions for codewords c are balls B ρ( c ), where ρ = r 1 or ρ = r 2. These are called ( r 1, r 2)-error-correcting codes. If these balls are not only disjoint but also partition the space of all words, then C is called perfect. We are especially interested in codes with the property that centers of balls with the same radius r i are at least 2 r i + 2 apart ( i = 1, 2). These are called bipartite codes. Our main theorem states that a bipartite perfect ( r, 1)-error-correcting code with r ⩾ 2 must have r = 2 and in fact is obtained from a code with the parameters of a Preparata code.
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