Perfect modes with distinct protective radii

J.M. van den Akker, J.H. Koolen, R.J.M. Vaessens
1990 Discrete Mathematics  
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,
more » ... correcting code with r 3 2 must have r = 2 and in fact is obtained from a code with the parameters of a Preparata code. 0012-365X/90/$3.50 0 1990, Elsevier Science Publishers B.V. (North-Holland)
doi:10.1016/0012-365x(90)90184-j fatcat:b5b4yrzcbrh75dseblxtyvh7um