Characterization of Perfect Ulam Permutation Codes via Spheres and Young Tableaux (Combinatorics of Lie Type)

Abstract

Permutation codes in the Ulam metric have recently been proposed for use in flash memory devices. We explore the possibility of perfect permutation codes in the Ulam metric by considering sphere sizes of permutations in the Ulam metric. We also introduce new a method to calculate exact sphere sizes using Young Tableaux. The discussion is then extended to multipermutation codes, where we consider sphere sizes toward understanding perfect Ulam multipermutation codes.