Permutation Arrays Under the Chebyshev Distance

TL;DR

This paper explores permutation arrays under the Chebyshev distance, providing new constructions and bounds, motivated by applications in power line communication and flash memory storage.

Contribution

It introduces novel constructions and bounds for permutation arrays using the Chebyshev metric, expanding their applicability in communication systems.

Findings

New constructions of permutation arrays under Chebyshev distance

Bounds on the size of permutation arrays with Chebyshev metric

Applications to power line communication and flash memories

Abstract

An (n,d) permutation array (PA) is a set of permutations of length n with the property that the distance (under some metric) between any two permutations in the array is at least d. They became popular recently for communication over power lines. Motivated by an application to flash memories, in this paper the metric used is the Chebyshev metric. A number of different constructions are given as well as bounds on the size of such PA.