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
SN - 0925-1022
VL - 32
SP - 51
EP - 64
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 1-3
ER -