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We consider codes C for which the decoding regions for codewords c are balls B"(c), where p = r, or p = r,. These are called (r" r,)-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 '; are at least 2r; + 2 apart (i = 1, 2). These are called bipartite codes. Our main theorem states that a bipartite perfect (r,doi:10.1016/0012-365x(90)90184-j fatcat:b5b4yrzcbrh75dseblxtyvh7um