Three mutually orthogonal idempotent Latin squares of orders 22 and 26

1996 ◽  
Vol 51 (2) ◽  
pp. 101-106 ◽  
Author(s):  
R.J.R. Abel ◽  
Xiafu Zhang ◽  
Hangfu Zhang
Keyword(s):  
Latin Squares ◽  
Orthogonal Idempotent

scholarly journals Further results on incomplete (3,2,1)- conjugate orthogonal idempotent Latin squares

1990 ◽  
Vol 84 (1) ◽  
pp. 1-14 ◽  
Author(s):  
F.E. Bennett ◽  
Lisheng Wu ◽  
L. Zhu
Keyword(s):  
Latin Squares ◽  
Orthogonal Idempotent

scholarly journals Incomplete conjugate orthogonal idempotent latin squares

1987 ◽  
Vol 65 (1) ◽  
pp. 5-21 ◽  
Author(s):  
F.E Bennett ◽  
L Zhu
Keyword(s):  
Latin Squares ◽  
Orthogonal Idempotent

On Maximal Sets of Mutually Orthogonal Idempotent Latin Squares

1971 ◽  
Vol 14 (3) ◽  
pp. 449-449 ◽  
Author(s):  
N. S. Mendelsohn
Keyword(s):  
Prime Power ◽  
Latin Squares ◽  
Orthogonal Idempotent ◽  
Trivial Fact

It is a well-known trivial fact that for a given integer n there exists at most n — 2 pairwise orthogonal idempotent latin squares. In the following note we prove that for n a prime power there always exists n—2 such squares.

scholarly journals A Discussion of a Cryptographical Scheme Based in F-Critical Sets of a Latin Square

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 285
Author(s):  
Laura M. Johnson ◽  
Stephanie Perkins
Keyword(s):  
Necessary Conditions ◽  
Latin Square ◽  
Latin Squares ◽  
Critical Sets ◽  
Long Cycles ◽  
The Given

This communication provides a discussion of a scheme originally proposed by Falcón in a paper entitled “Latin squares associated to principal autotopisms of long cycles. Applications in cryptography”. Falcón outlines the protocol for a cryptographical scheme that uses the F-critical sets associated with a particular Latin square to generate access levels for participants of the scheme. Accompanying the scheme is an example, which applies the protocol to a particular Latin square of order six. Exploration of the example itself, revealed some interesting observations about both the structure of the Latin square itself and the autotopisms associated with the Latin square. These observations give rise to necessary conditions for the generation of the F-critical sets associated with certain autotopisms of the given Latin square. The communication culminates with a table which outlines the various access levels for the given Latin square in accordance with the scheme detailed by Falcón.

Latin squares from multiplication tables

2021 ◽  
Author(s):  
Michał Dębski ◽  
Jarosław Grytczuk
Keyword(s):  
Latin Squares ◽  
Multiplication Tables

Critical Sets of Full n-Latin Squares

2015 ◽  
Vol 32 (2) ◽  
pp. 543-552 ◽  
Author(s):  
Nicholas J. Cavenagh ◽  
Vaipuna Raass
Keyword(s):  
Latin Squares ◽  
Critical Sets

90.73 Powers of Latin squares

2006 ◽  
Vol 90 (519) ◽  
pp. 478-481 ◽  
Author(s):  
Emanuel Emanouilidis
Keyword(s):  
Latin Squares

Low-Power, Resilient Interconnection with Orthogonal Latin Squares

2011 ◽  
Vol 28 (2) ◽  
pp. 30-39 ◽  
Author(s):  
Seung Eun Lee ◽  
Yoon Seok Yang ◽  
G S Choi ◽  
Wei Wu ◽  
R Iyer
Keyword(s):  
Low Power ◽  
Latin Squares ◽  
Orthogonal Latin Squares
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