TY - JOUR

T1 - Constructions for permutation codes in powerline communications

AU - Chu, Wensong

AU - Colbourn, Charles

AU - Dukes, Peter

N1 - Funding Information:
The authors thank Manish Gupta and Alan C. H. Ling for fruitful conversations on this topic. The authors research is supported by the Army Research Office under grant number DAAD 19-01-1-0406.

PY - 2004/5

Y1 - 2004/5

N2 - A permutation array (or code) of length n and distance d is a set Γ of permutations from some fixed set of n symbols such that the Hamming distance between each distinct x, y ∈ Γ is at least d. One motivation for coding with permutations is powerline communication. After summarizing known results, it is shown here that certain families of polynomials over finite fields give rise to permutation arrays. Additionally, several new computational constructions are given, often making use of automorphism groups. Finally, a recursive construction for permutation arrays is presented, using and motivating the more general notion of codes with constant weight composition.

AB - A permutation array (or code) of length n and distance d is a set Γ of permutations from some fixed set of n symbols such that the Hamming distance between each distinct x, y ∈ Γ is at least d. One motivation for coding with permutations is powerline communication. After summarizing known results, it is shown here that certain families of polynomials over finite fields give rise to permutation arrays. Additionally, several new computational constructions are given, often making use of automorphism groups. Finally, a recursive construction for permutation arrays is presented, using and motivating the more general notion of codes with constant weight composition.

KW - Constant composition code

KW - Heuristic search

KW - Permutation array

KW - Permutation code

KW - Permutation polynomial

KW - Reactive local search

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U2 - 10.1023/B:DESI.0000029212.52214.71

DO - 10.1023/B:DESI.0000029212.52214.71

M3 - Article

AN - SCOPUS:3543117778

VL - 32

SP - 51

EP - 64

JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

SN - 0925-1022

IS - 1-3

ER -