Abstract
The concept of the combinatorial matrix of an unrestricted code and the notion of anr-partition design admitted by a code are introduced and discussed in detail. The theory includes a characterization of completely regular codes, and a combinatorial interpretation of the fact that the distinct rows of the distance distribution matrix of a code are linearly independent. In general, it is possible to compute the distance distribution matrix of any code admitting a given partition design by solving a well-defined system of linear equations; this is an efficient technique provided the number of classes in the partition is relatively small.
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Camion, P., Courteau, B. & Delsarte, P. Onr-partition designs in hamming spaces. AAECC 2, 147–162 (1992). https://doi.org/10.1007/BF01294330
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DOI: https://doi.org/10.1007/BF01294330