Frequency permutation arrays

Sophie Huczynska, Gary Lee Mullen

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

Motivated by recent interest in permutation arrays, we introduce and investigate the more general concept of frequency permutation arrays (FPAs). An FPA of length n - mX and distance d is a set T of multipermutations on a multiset of m symbols, each repeated with frequency λ, such that the Hamming distance between any distinct x,y ∈ T is at least d. Such arrays have potential applications in powerline communication. In this article, we establish basic properties of FPAs, and provide direct constructions for FPAs using a range of combinatorial objects, including polynomials over finite fields, combinatorial designs, and codes. We also provide recursive constructions, and give bounds for the maximum size of such arrays.

Original languageEnglish (US)
Pages (from-to)463-478
Number of pages16
JournalJournal of Combinatorial Designs
Volume14
Issue number6
DOIs
StatePublished - Nov 1 2006

Fingerprint

Permutation
Combinatorial Design
Hamming Distance
Multiset
Galois field
Distinct
Polynomial
Range of data

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics

Cite this

Huczynska, Sophie ; Mullen, Gary Lee. / Frequency permutation arrays. In: Journal of Combinatorial Designs. 2006 ; Vol. 14, No. 6. pp. 463-478.
@article{1d8957623d5648bbbcc500b501510370,
title = "Frequency permutation arrays",
abstract = "Motivated by recent interest in permutation arrays, we introduce and investigate the more general concept of frequency permutation arrays (FPAs). An FPA of length n - mX and distance d is a set T of multipermutations on a multiset of m symbols, each repeated with frequency λ, such that the Hamming distance between any distinct x,y ∈ T is at least d. Such arrays have potential applications in powerline communication. In this article, we establish basic properties of FPAs, and provide direct constructions for FPAs using a range of combinatorial objects, including polynomials over finite fields, combinatorial designs, and codes. We also provide recursive constructions, and give bounds for the maximum size of such arrays.",
author = "Sophie Huczynska and Mullen, {Gary Lee}",
year = "2006",
month = "11",
day = "1",
doi = "10.1002/jcd.20096",
language = "English (US)",
volume = "14",
pages = "463--478",
journal = "Journal of Combinatorial Designs",
issn = "1063-8539",
publisher = "John Wiley and Sons Inc.",
number = "6",

}

Frequency permutation arrays. / Huczynska, Sophie; Mullen, Gary Lee.

In: Journal of Combinatorial Designs, Vol. 14, No. 6, 01.11.2006, p. 463-478.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Frequency permutation arrays

AU - Huczynska, Sophie

AU - Mullen, Gary Lee

PY - 2006/11/1

Y1 - 2006/11/1

N2 - Motivated by recent interest in permutation arrays, we introduce and investigate the more general concept of frequency permutation arrays (FPAs). An FPA of length n - mX and distance d is a set T of multipermutations on a multiset of m symbols, each repeated with frequency λ, such that the Hamming distance between any distinct x,y ∈ T is at least d. Such arrays have potential applications in powerline communication. In this article, we establish basic properties of FPAs, and provide direct constructions for FPAs using a range of combinatorial objects, including polynomials over finite fields, combinatorial designs, and codes. We also provide recursive constructions, and give bounds for the maximum size of such arrays.

AB - Motivated by recent interest in permutation arrays, we introduce and investigate the more general concept of frequency permutation arrays (FPAs). An FPA of length n - mX and distance d is a set T of multipermutations on a multiset of m symbols, each repeated with frequency λ, such that the Hamming distance between any distinct x,y ∈ T is at least d. Such arrays have potential applications in powerline communication. In this article, we establish basic properties of FPAs, and provide direct constructions for FPAs using a range of combinatorial objects, including polynomials over finite fields, combinatorial designs, and codes. We also provide recursive constructions, and give bounds for the maximum size of such arrays.

UR - http://www.scopus.com/inward/record.url?scp=33750503204&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750503204&partnerID=8YFLogxK

U2 - 10.1002/jcd.20096

DO - 10.1002/jcd.20096

M3 - Article

VL - 14

SP - 463

EP - 478

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

SN - 1063-8539

IS - 6

ER -