A New Construction of Permutation Arrays

Jung Youl PARK; Hong-Yeop SONG

doi:10.1587/transfun.E95.A.1855

A New Construction of Permutation Arrays

Jung Youl PARK, Hong-Yeop SONG

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Let PA(n, d) be a permutation array (PA) of order n and the minimum distance d. We propose a new construction of the permutation array PA(p^m, p^m-1k) for a given prime number p, a positive integer k < p and a positive integer m. The resulted array has (|PA(p,k)|p^(m-1)(p-k))^m rows. Compared to the other constructions, the new construction gives a permutation array of far bigger size with a large minimum distance, for example, when k ≥ 2p/3. Moreover the proposed construction provides an algorithm to find the i-th row of PA (p^m, p^m-1k) for a given index i very simply.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E95-A No.11 pp.1855-1861

Publication Date: 2012/11/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E95.A.1855

Type of Manuscript: Special Section PAPER (Special Section on Signal Design and Its Applications in Communications)

Category: Sequences

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Jung Youl PARK, Hong-Yeop SONG, "A New Construction of Permutation Arrays" in IEICE TRANSACTIONS on Fundamentals, vol. E95-A, no. 11, pp. 1855-1861, November 2012, doi: 10.1587/transfun.E95.A.1855.
Abstract: Let PA(n, d) be a permutation array (PA) of order n and the minimum distance d. We propose a new construction of the permutation array PA(p^m, p^m-1k) for a given prime number p, a positive integer k < p and a positive integer m. The resulted array has (|PA(p,k)|p^(m-1)(p-k))^m rows. Compared to the other constructions, the new construction gives a permutation array of far bigger size with a large minimum distance, for example, when k ≥ 2p/3. Moreover the proposed construction provides an algorithm to find the i-th row of PA (p^m, p^m-1k) for a given index i very simply.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E95.A.1855/_p

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@ARTICLE{e95-a_11_1855,
author={Jung Youl PARK, Hong-Yeop SONG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A New Construction of Permutation Arrays},
year={2012},
volume={E95-A},
number={11},
pages={1855-1861},
abstract={Let PA(n, d) be a permutation array (PA) of order n and the minimum distance d. We propose a new construction of the permutation array PA(p^m, p^m-1k) for a given prime number p, a positive integer k < p and a positive integer m. The resulted array has (|PA(p,k)|p^(m-1)(p-k))^m rows. Compared to the other constructions, the new construction gives a permutation array of far bigger size with a large minimum distance, for example, when k ≥ 2p/3. Moreover the proposed construction provides an algorithm to find the i-th row of PA (p^m, p^m-1k) for a given index i very simply.},
keywords={},
doi={10.1587/transfun.E95.A.1855},
ISSN={1745-1337},
month={November},}

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TY - JOUR
TI - A New Construction of Permutation Arrays
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1855
EP - 1861
AU - Jung Youl PARK
AU - Hong-Yeop SONG
PY - 2012
DO - 10.1587/transfun.E95.A.1855
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E95-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2012
AB - Let PA(n, d) be a permutation array (PA) of order n and the minimum distance d. We propose a new construction of the permutation array PA(p^m, p^m-1k) for a given prime number p, a positive integer k < p and a positive integer m. The resulted array has (|PA(p,k)|p^(m-1)(p-k))^m rows. Compared to the other constructions, the new construction gives a permutation array of far bigger size with a large minimum distance, for example, when k ≥ 2p/3. Moreover the proposed construction provides an algorithm to find the i-th row of PA (p^m, p^m-1k) for a given index i very simply.
ER -