The geometry of sets of orthogonal frequency hypercubes

V. C. Mavron; Thomas McDonough; Gary L. Mullen

doi:10.1002/jcd.20135

The geometry of sets of orthogonal frequency hypercubes

V. C. Mavron, Thomas McDonough, Gary L. Mullen

Adran Ffiseg

Pennsylvania State University

Allbwn ymchwil: Cyfraniad at gyfnodolyn › Erthygl › adolygiad gan gymheiriaid

1 Dyfyniad (Scopus)

168 Wedi eu Llwytho i Lawr (Pure)

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We extend the notion of a framed net, introduced by D. Jungnickel, V. C. Mavron, and T. P. McDonough, J Combinatorial Theory A, 96 (2001), 376–387, to that of a d-framed net of type ℓ, where d ≥ 2 and 1 ≤ ℓ ≤ d-1, and we establish a correspondence between d-framed nets of type ℓ and sets of mutually orthogonal frequency hypercubes of dimension d. We provide a new proof of the maximal size of a set of mutually orthogonal frequency hypercubes of type ℓ and dimension d, originally established by C. F. Laywine, G. L. Mullen, and G. Whittle, Monatsh Math 119 (1995), 223–238, and we obtain a geometric characterization of the framed net when this bound is satisfied as a PBIBD based on a d-class association Hamming scheme H(d,n).

Iaith wreiddiol	Saesneg
Tudalennau (o-i)	449-459
Nifer y tudalennau	11
Cyfnodolyn	Journal of Combinatorial Designs
Cyfrol	15
Rhif cyhoeddi	6
Dynodwyr Gwrthrych Digidol (DOIs)	https://doi.org/10.1002/jcd.20135
Statws	Cyhoeddwyd - Tach 2006

Mynediad at Ddogfen

10.1002/jcd.20135

frequency-hypercubes-postprint.pdf

http://hdl.handle.net/2160/5984

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@article{caf0d9a978c749c2bddc07a0dcc7c157,

title = "The geometry of sets of orthogonal frequency hypercubes",

abstract = "We extend the notion of a framed net, introduced by D. Jungnickel, V. C. Mavron, and T. P. McDonough, J Combinatorial Theory A, 96 (2001), 376–387, to that of a d-framed net of type ℓ, where d ≥ 2 and 1 ≤ ℓ ≤ d-1, and we establish a correspondence between d-framed nets of type ℓ and sets of mutually orthogonal frequency hypercubes of dimension d. We provide a new proof of the maximal size of a set of mutually orthogonal frequency hypercubes of type ℓ and dimension d, originally established by C. F. Laywine, G. L. Mullen, and G. Whittle, Monatsh Math 119 (1995), 223–238, and we obtain a geometric characterization of the framed net when this bound is satisfied as a PBIBD based on a d-class association Hamming scheme H(d,n).",

keywords = "frequency hypercubes, affine geometry, framed net, Hamming scheme",

author = "Mavron, {V. C.} and Thomas McDonough and Mullen, {Gary L.}",

note = "V.C. Mavron, T.P. McDonough, Gary L. Mullen, The geometry of sets of orthogonal frequency hypercubes. Journal of Combinatorial Designs, Volume 15, Issue 6, pages 449–459, November 2007.",

year = "2006",

month = nov,

doi = "10.1002/jcd.20135",

language = "English",

volume = "15",

pages = "449--459",

journal = "Journal of Combinatorial Designs",

issn = "1520-6610",

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TY - JOUR

T1 - The geometry of sets of orthogonal frequency hypercubes

AU - Mavron, V. C.

AU - McDonough, Thomas

AU - Mullen, Gary L.

N1 - V.C. Mavron, T.P. McDonough, Gary L. Mullen, The geometry of sets of orthogonal frequency hypercubes. Journal of Combinatorial Designs, Volume 15, Issue 6, pages 449–459, November 2007.

PY - 2006/11

Y1 - 2006/11

N2 - We extend the notion of a framed net, introduced by D. Jungnickel, V. C. Mavron, and T. P. McDonough, J Combinatorial Theory A, 96 (2001), 376–387, to that of a d-framed net of type ℓ, where d ≥ 2 and 1 ≤ ℓ ≤ d-1, and we establish a correspondence between d-framed nets of type ℓ and sets of mutually orthogonal frequency hypercubes of dimension d. We provide a new proof of the maximal size of a set of mutually orthogonal frequency hypercubes of type ℓ and dimension d, originally established by C. F. Laywine, G. L. Mullen, and G. Whittle, Monatsh Math 119 (1995), 223–238, and we obtain a geometric characterization of the framed net when this bound is satisfied as a PBIBD based on a d-class association Hamming scheme H(d,n).

AB - We extend the notion of a framed net, introduced by D. Jungnickel, V. C. Mavron, and T. P. McDonough, J Combinatorial Theory A, 96 (2001), 376–387, to that of a d-framed net of type ℓ, where d ≥ 2 and 1 ≤ ℓ ≤ d-1, and we establish a correspondence between d-framed nets of type ℓ and sets of mutually orthogonal frequency hypercubes of dimension d. We provide a new proof of the maximal size of a set of mutually orthogonal frequency hypercubes of type ℓ and dimension d, originally established by C. F. Laywine, G. L. Mullen, and G. Whittle, Monatsh Math 119 (1995), 223–238, and we obtain a geometric characterization of the framed net when this bound is satisfied as a PBIBD based on a d-class association Hamming scheme H(d,n).

KW - frequency hypercubes

KW - affine geometry

KW - framed net

KW - Hamming scheme

U2 - 10.1002/jcd.20135

DO - 10.1002/jcd.20135

M3 - Article

SN - 1520-6610

VL - 15

SP - 449

EP - 459

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

IS - 6

ER -

The geometry of sets of orthogonal frequency hypercubes

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