• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.285-293
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• 2006

Let X be a n-set and let A = [aij] be a $n {\times} n$ matrix for which $aij {\subseteq} X$, for $1 {\le} i,\;j {\le} n$. A is called a generalized Latin square on X, if the following conditions is satisfied: $U^n_{i=1}\;aij = X = U^n_{j=1}\;aij$. In this paper, we prove that every generalized Latin square has an orthogonal mate and introduce a Hv-structure on a set of generalized Latin squares. Finally, we prove that every generalized Latin square of order n, has a transversal set.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.21-31
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• 2010

A latin square of order n is an $n{\times}n$ array with entries from a set of n numbers arrange in such a way that each number occurs exactly once in each row and exactly once in each column. Two latin squares of the same order are orthogonal latin square if the two latin squares are superimposed, then the $n^2$ cells contain each pair consisting of a number from the first square and a number from the second. In Europe, Orthogonal Latin squares are the mathematical concepts attributed to Euler. However, an Euler square of order nine was already in existence prior to Euler in Korea. It appeared in the monograph Koo-Soo-Ryak written by Choi Seok-Jeong(1646-1715). He construct a magic square by using two orthogonal latin squares for the first time in the world. In this paper, we explain Choi' s orthogonal latin squares and the history of the Orthogonal Latin squares.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.5D
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• pp.623-631
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• 2011

In this study, a new method which can detect incidents in interrupted traffic flow was suggested. The applied method of detecting the incident is the Latin Square Analysis Method by using traffic traits. In the Latin Square Analysis, unlike other previously tried methods, the traffic situation was analyzed, this time considering the changes in traffic traits for each lane and for each time period. The data used in this study were the data observed in the actual field with fine weather. The traffic volumes, the vehicle speed and the occupancy rate were collected on the interrupted flow road. The data were collected in normal and incident situations. The incidents occurred on the second lane, the time of persistent incidents was set to 10 minutes. The Latin Square Analyses were performed using the collected data with the traffic volume, with the vehicle speed or with the occupancy rate. As a result in this study, in case of detecting the traffic situations with Latin Square Analysis, it will be more successful to apply traffic volume to detect the traffic situations than to apply other factors.

• Journal of the Korean Home Economics Association
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• v.23 no.3
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• pp.49-53
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• 1985

The typical texture profile analysis of acorn flour gel was investigated with Instron univ. testing machine by two experimental designs, 3$\times$3 latin square and $3^{3}$factorial experiment. As the result, it was revealed that Latin square is a useful method to reduce the number of experiments, in the case of a negligible interaction.

• Journal of Information Processing Systems
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• v.9 no.3
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• pp.499-510
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• 2013

Hardware-Software co-simulation of a multiple image encryption technique shall be described in this paper. Our proposed multiple image encryption technique is based on the Latin Square Image Cipher (LSIC). First, a carrier image that is based on the Latin Square is generated by using 256-bits of length key. The XOR operation is applied between an input image and the Latin Square Image to generate an encrypted image. Then, the XOR operation is applied between the encrypted image and the second input image to encrypt the second image. This process is continues until the nth input image is encrypted. We achieved hardware co-simulation of the proposed multiple image encryption technique by using the Xilinx System Generator (XSG). This encryption technique is modeled using Simulink and XSG Block set and synthesized onto Virtex 2 pro FPGA device. We validated our proposed technique by using the hardware software co-simulation method.

• Communications of Mathematical Education
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• v.6
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• pp.371-381
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• 1997

Let p be an odd prime number. We introduce simple and useful decoding algorithm for orthogonal Latin square codes of order p. Let H be the parity check matrix of orthogonal Latin square code. For any x ${\in}$ GF(p)$^{n}$, we call xH$^{T}$ the syndrome of x. This method is based on the syndrome decoding for linear codes. In L$_{p}$, we need to find the first and the second coordinates of codeword in order to correct the errored received vector.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.91-113
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• 2023

The polytope of tristochastic tensors of degree three, the Latin polytope, has two kinds of extreme points. Those that are at a maximum distance from the barycenter of the polytope correspond to Latin squares. The remaining extreme points are said to be short. The aim of the paper is to determine the geometry of these short extreme points, as they relate to the Latin squares. The paper adapts the Latin square notion of an intercalate to yield the new concept of a cross-intercalate between two Latin squares. Cross-intercalates of pairs of orthogonal Latin squares of degree three are used to produce the short extreme points of the degree three Latin polytope. The pairs of orthogonal Latin squares fall into two classes, described as parallel and reversed, each forming an orbit under the isotopy group. In the inverse direction, we show that each short extreme point of the Latin polytope determines four pairs of orthogonal Latin squares, two parallel and two reversed.

• Journal of Korea Multimedia Society
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• v.18 no.9
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• pp.1083-1090
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• 2015

A generalized recursive circulant network(GR) is widely used in the design and implementation of local area networks and parallel processing architectures. In this paper, we investigate the routing of a message on this network, that is a key to the performance of this network. We would like to transmit maximum number of packets from a source node to a destination node simultaneously along paths on this network, where the i^th packet traverses along the i^th path. In order for all packets to arrive at the destination node securely, the i^th path must be node-disjoint from all other paths. For construction of these paths, employing the Hamiltonian Circuit Latin Square(HCLS), a special class of (n x n) matrices, we present O(n²) parallel routing algorithm on generalized recursive circulant networks.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2004.10a
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• pp.433-438
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• 2004

The rapid machining of prototypes plays an important role in product process. Rapid Prototyping(RP) is the widespread technology to produce prototype. But, it have many problems such as shrinkage, deformation and formation occurred by hardening of resin and stair shaping, On the contrary, high speed machining(HSM) technology has many advantages such as good quality, low cost and rapid machining time. Moreover, it is possible to use the material of original product. This paper presents manufacture of trial product by HSM and optimization of machining condition for high productivity in the view of manufacturing time and average error. For example, propeller is machined by the surface machining of thin surface parts. Experiments are designed of machining conditions by Latin Square method and machining condition is optimized and selected by ANOVA

• Journal of the Korean Society for Precision Engineering
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• v.22 no.10 s.175
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• pp.99-106
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• 2005

This paper presents manufacture of mock-up by HSM and optimization of machining condition for high productivity in the view of manufacturing time and accuracy. The rapid machining of prototypes plays an important role in building mock-up. Rapid Prototyping(RP) is a technology to make prototype. But, it have many problems such as shrinkage. deformation and formation occurred by hardening of resin and stair shaping. On the contrary, high speed machining(HSM) technology has many advantages such as good quality, low cost and rapid machining time. HSM and RP is compared for machining efficiency. Experiments are designed by Latin Square Method and machining condition is optimized and selected by ANOVA. For example, propeller is machined by the surface machining of thin surface parts.