Permutation codes, in the form of rank modulation, have shown promise forapplications such as flash memory. One of the metrics recently suggested asappropriate for rank modulation is the Ulam metric, which measures the minimumtranslocation distance between permutations. Multipermutation codes have alsobeen proposed as a generalization of permutation codes that would improve codesize (and consequently the code rate). In this paper we analyze the Ulam metricin the context of multipermutations, noting some similarities and differencesbetween the Ulam metric in the context of permutations. We also consider spheresizes for multipermutations under the Ulam metric and resulting bounds on codesize.
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