Direct constructions for general families of cyclic mutually nearly orthogonal Latin squares

Demirkale, Faith, Donovan, Diane and Khodkar, Abdollah (2015) Direct constructions for general families of cyclic mutually nearly orthogonal Latin squares. Journal of Combinatorial Designs, 23 5: 195-203. doi:10.1002/jcd.21394


Author Demirkale, Faith
Donovan, Diane
Khodkar, Abdollah
Title Direct constructions for general families of cyclic mutually nearly orthogonal Latin squares
Journal name Journal of Combinatorial Designs   Check publisher's open access policy
ISSN 1520-6610
1063-8539
Publication date 2015-05
Year available 2014
Sub-type Article (original research)
DOI 10.1002/jcd.21394
Open Access Status
Volume 23
Issue 5
Start page 195
End page 203
Total pages 9
Place of publication Hoboken NJ, United States
Publisher John Wiley & Sons
Collection year 2015
Language eng
Formatted abstract
Two Latin squares L = [l(i, j)] and M = [m(i, j)], of even order n with entries {0, 1, 2, . . . , n − 1}, are said to be nearly orthogonal if the superimposition of L on M yields an n × n array A = [(l(i, j ),m(i, j))] in which each ordered pair (x, y), 0 ≤ x, y n − 1 and xy, occurs at least once and the ordered pair (x, x + n/2) occurs exactly twice. In this paper, we present direct constructions for the existence of general families of three cyclic mutually orthogonal Latin squares of orders 48k + 14, 48k + 22, 48k + 38, and 48k + 46. The techniques employed are based on the principle of Methods of Differences and so we also establish infinite classes of “quasi-difference” sets for these orders.
Keyword Latin squares
Nearly orthogonal Latin squares
Orthogonal Latin squares
Quasi-difference sets
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published online ahead of print 29 April 2014

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
 
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