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- W2111220890 abstract "Codes over permutations under the infinity norm have been recently suggested as a coding scheme for correcting limited-magnitude errors in the rank modulation scheme. Given such a code, we show that a simple relabeling operation, which produces an isomorphic code, may drastically change the minimal distance of the code. Thus, we may choose a code structure for efficient encoding/decoding procedures, and then optimize the code's minimal distance via relabeling. We formally define the relabeling problem, and show that all codes may be relabeled to get a minimal distance at most 2. The decision problem of whether a code may be relabeled to distance 1 is shown to be NP-complete, and calculating the best achievable minimal distance after relabeling is proved hard to approximate. Finally, we consider general bounds on the relabeling problem. We specifically show the optimal relabeling distance of cyclic groups. A specific case of a general probabilistic argument is used to show AGL(p) may be relabeled to a minimal distance of p - O(√(p ln p))." @default.
- W2111220890 created "2016-06-24" @default.
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- W2111220890 date "2011-07-01" @default.
- W2111220890 modified "2023-09-27" @default.
- W2111220890 title "On the labeling problem of permutation group codes under the infinity metric" @default.
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- W2111220890 doi "https://doi.org/10.1109/isit.2011.6034263" @default.
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