Abstract
We discuss two distance concepts between q-ary n-sequences, 2 ≤ q < n, called partition distances. This distances are metrics in the space of all partitions of a finite n-set. For the metrics, we study codes called q-partition codes and present a construction of these codes based on the first order Reed–Muller codes. A random coding bound is obtained. We also work out an application of q-partition codes to the statistical analysis of psychological or medical tests using questionnaires.
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