Autoparatopisms of Quasigroups and Latin Squares
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DOI: 10.1002/jcd.21515
Abstract: Paratopism is a well-known action of the wreath product Sn≀S3 on Latin squares of order n. A paratopism that maps a Latin square to itself is an autoparatopism of that Latin square. Let Par(n) denote… read more here.
Keywords: autoparatopisms quasigroups; latin squares; latin square; quasigroups latin ... See more keywords
On the Distances between Latin Squares and the Smallest Defining Set Size
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DOI: 10.1002/jcd.21529
Abstract: In this note, we show that for each Latin square L of order n≥2, there exists a Latin square L′≠L of order n such that L and L′ differ in at most 8n cells. Equivalently,… read more here.
Keywords: smallest defining; distances latin; square order; size ... See more keywords
Equitable partitions of Latin-square graphs
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Combinatorial Designs"
DOI: 10.1002/jcd.21634
Abstract: Funding: R.A. Bailey and Peter J. Cameron are grateful to Shanghai Jiao Tong University for funding, from the National Science Foundation of China (11671258) and STCSM (17690740800), a research visit where part of this study… read more here.
Keywords: partitions latin; equitable partitions; latin square; square graphs ... See more keywords
All group‐based latin squares possess near transversals
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DOI: 10.1002/jcd.21701
Abstract: In a latin square of order n, a near transversal is a collection of n −1 cells which intersects each row, column, and symbol class at most once. A longstanding conjecture of Brualdi, Ryser, and Stein… read more here.
Keywords: group; latin squares; based latin; latin square ... See more keywords
Reliability of 3D memories using Orthogonal Latin Square codes
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DOI: 10.1016/j.microrel.2019.03.001
Abstract: Abstract Radiation is a cause of errors in electronics systems, especially on those deployed in space. Memories can suffer from different radiation effects including Single Event Upsets and Multiple Cell Upsets. These effects produce corruption… read more here.
Keywords: latin square; orthogonal latin; reliability memories; square codes ... See more keywords
A note on the construction of Latin square type designs
Sign Up to like & getrecommendations! Published in 2020 at "Communications in Statistics - Theory and Methods"
DOI: 10.1080/03610926.2020.1734837
Abstract: Abstract A PBIB design based on L2 association scheme with parameters: has been constructed in literature using mutually orthogonal Latin squares (MOLS). In this note we are presenting an alternative method of construction of such… read more here.
Keywords: note construction; construction latin; construction; type designs ... See more keywords
Interference Alignment Schemes Using Latin Square for $K\times3$ MIMO X Channel
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DOI: 10.1109/access.2018.2888501
Abstract: In this paper, we study an interference alignment (IA) scheme with finite time extension and beamformer selection method with low computational complexity for X channel. An IA scheme with a chain structure by the Latin… read more here.
Keywords: alignment schemes; beamformer selection; latin square; interference alignment ... See more keywords
A New Chaotic Image Encryption Algorithm Based on Transversals in a Latin Square
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DOI: 10.3390/e24111574
Abstract: In this paper, a new combinatorial structure is introduced for image encryption, which has an excellent encryption effect on security and efficiency. An n-transversal in a Latin square has the function of classifying all the… read more here.
Keywords: latin square; encryption; image encryption; latin squares ... See more keywords
Trivial and Nontrivial Eigenvectors for Latin Squares in Max-Plus Algebra
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DOI: 10.3390/sym14061101
Abstract: A square array whose all rows and columns are different permutations of the same length over the same symbol set is known as a Latin square. A Latin square may or may not be symmetric.… read more here.
Keywords: latin square; latin squares; trivial nontrivial; nontrivial eigenvectors ... See more keywords