In the rank modulation scheme for flash memories, permutation codes have been studied. In
this paper, we study perfect permutation codes in S_n S n, the set of all permutations on n …

We give two methods that are based on the representation theory of symmetric groups to
study the largest size P (n, d) of permutation codes of length n, ie, subsets of the set S n of all …

This paper concerns the construction and hardware execution of (n, n (n-1), n-1) permutation
group codes (PGCs) for communication systems. Cyclic shift techniques acting on a …

Permutation arrays under the Kendall-τ metric have been considered for error-correcting
codes. Given n and d∈[1,(n 2)], the task is to find a large permutation array of permutations …

We investigate the maximum cardinality and the mathematical structure of error-correcting
codes endowed with the Kendall-$\tau $ metric. We establish an averaging bound for the …

The Cayley distance between two permutations $\pi,\sigma\in S_n $ is the minimum number
of\textit {transpositions} required to obtain the permutation $\sigma $ from $\pi $. When we …

In order to overcome the challenges posed by flash memories, the rank modulation scheme
was proposed. In the rank modulation the codewords are permutations. In this paper, we …

Permutation codes are error-correcting codes over symmetric groups. We focus on
permutation codes under Chebyshev (l∞) distance. A permutation code invented by Kløve …

We study $ P (n, 3) $, the size of the largest subset of the set of all permutations $ S_n $ with
minimum Kendall $\tau $-distance $3 $. Using a combination of group theory and integer …

Kløve et al. proposed permutation codes under Chebyshev distance and iterative encoding
and decoding algorithms for the permutation code. In this paper, we introduce a factor graph …