Diagonally Neighbour Transitive Codes and Frequency Permutation Arrays

TL;DR

This paper characterizes a family of neighbour transitive codes in Hamming graphs, focusing on frequency permutation arrays, and classifies permutation codes generated by groups within this family, relevant for powerline communication.

Contribution

It introduces a new family of neighbour transitive codes involving frequency permutation arrays and classifies related permutation codes.

Findings

Characterization of neighbour transitive codes with frequency permutation arrays

Classification of permutation codes generated by groups in this family

Relevance to powerline communication noise problems

Abstract

Constant composition codes have been proposed as suitable coding schemes to solve the narrow band and impulse noise problems associated with powerline communication. In particular, a certain class of constant composition codes called frequency permutation arrays have been suggested as ideal, in some sense, for these purposes. In this paper we characterise a family of neighbour transitive codes in Hamming graphs in which frequency permutation arrays play a central rode. We also classify all the permutation codes generated by groups in this family.