2017/01/14 by Justin Kong, Kong, Justin, Manabu Hagiwara +1
Computer Science · Engineering · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.CO #math.IT
paper · pdf · doi:10.48550/arxiv.1701.03896
arxiv created 2017/01/14 · openalex publication_date 2017/01/14 · arxiv updated 2017/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Permutation codes, in the form of rank modulation, have shown promise for applications such as flash memory. One of the metrics recently suggested as appropriate for rank modulation is the Ulam metric, which measures the minimum translocation distance between permutations. Multipermutation codes have also been proposed as a generalization of permutation codes that would improve code size (and consequently the code rate). In this paper we analyze the Ulam metric in the context of multipermutations, noting some similarities and differences between the Ulam metric in the context of permutations. We also consider sphere sizes for multipermutations under the Ulam metric and resulting bounds on code size.