• The Korean Journal of Applied Statistics
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• v.24 no.3
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• pp.505-513
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• 2011

Sudoku is a famous Latin-square-based number-placement puzzle. Mo and Xu (2008) proposed Sudoku square designs based on the idea of Sudoku. Using several Sudoku square designs which are mutually orthogonal, we can suggest the orthogonal Sudoku square designs with block effect discrimination.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.231-239
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• 2008

We obtain a necessary and sufficient condition for the existence of Mendelsohn triple systems excluding contiguous units with ${\lambda}$ = 1. Also, we obtain the spectrum for cyclic such systems.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.10
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• pp.5144-5160
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• 2019

Secret sharing is an effective way of protecting secret messages. However, the traditional secret sharing schemes are considered meaningless due to malicious people attention which might raise risks. To overcome the weakness, this paper presents an effective secret sharing scheme with the functionality of cheater identification, based on meaningful QR code. The secret message will be split and concealed in the padding region of cover QR codes with the assistance of Latin square and it can be completely restored when all the involved participants cooperate. The concealing strategy exploits the characteristic of Reed-Solomon (RS) code to ensure the strong robustness of generated QR code pseudo-shares. The meaningful QR code pseudo-shares help to reduce the curious of unrelated persons. Some experiments were done to evaluate the performance of proposed scheme. The results showed that the proposed scheme is feasible, efficient and secure compared to the other existing schemes. It also achieves a higher secret payload and maintains stronger robustness.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.12
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• pp.1357-1365
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• 1991

This paper proposes the generation of several classes of frequency hopping patterns. which are derived by permutation, for an asynchronous frequency hopping spread spectrum multiple accecss system (FH/SSMA). The first class of hopping patterns is obtained by using a Latin square. The second class of hopping patterns is derived by generalizing the first class which is designed by using a permutation technique. The third class of hopping patterns is designed by using a rotational base of elements. We evaluate the hit property of the proposed classes of hopping patterns when these patterns are nutually shifted in an FH/SSMA system. Compared to the Reed Slolmon sequences generated by the conventional method, the sequence obtained by the permutation technique can reduce the number of hits among hopping frequencies in asynchronous time/frequency shift.

• The Transactions of the Korea Information Processing Society
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• v.4 no.11
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• pp.2701-2710
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• 1997

Recursive circulant graph has recently developed as a new model of multiprocessors, and drawn considerable attention to supercomputing, In this paper, we investigate the routing of a message i recursive circulant, that is a key to the performance of this network. On recursive circulant network, we would like to transmit m packets from a source node to a destination node simultaneously along paths, where the ith packet will traverse along the ith path $(o{\leq}i{\leq}m-1)$. In oder for all packets to arrive at the destination node quickly and securely, the ith 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 $(n{\times}n)$ matrices, we present $O(n^2)$ parallel routing algorithm on recursive circulant network.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.617-642
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• 2022

For positive integers n and d with d < n, an n × n array A based on 𝒳 = {0, 1, …, nd} is called a sparse anti-magic square of order n with density d, denoted by SAMS(n, d), if each non-zero element of X occurs exactly once in A, and its row-sums, column-sums and two main diagonal-sums constitute a set of 2n + 2 consecutive integers. An SAMS(n, d) is called regular if there are exactly d non-zero elements in each row, each column and each main diagonal. In this paper, we investigate the existence of regular sparse anti-magic squares of order n ≡ 1, 5 (mod 6), and prove that there exists a regular SAMS(n, d) for any n ≥ 5, n ≡ 1, 5 (mod 6) and d with 2 ≤ d ≤ n - 1.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.10a
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• pp.578-579
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• 2009

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.667-674
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• 2013

Considering a special double-cover Q of the symmetric group of degree 3, we show that a proper non-regular approximate symmetry occurs from its quasigroup homogeneous space. The weak compatibility of any two elements of Q is completely characterized in any such quasigroup homogeneous space of degree 4.

• Journal of the Korean Statistical Society
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• v.8 no.2
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• pp.125-130
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• 1979

It is well known that $L_2(m)$ type PBIB designs have the Property A, so they are BNAS PBIB designs. However, $L_3(m)$ type PBIB designs are not of type of Property A but do have the factorial structure (Cotter, John, and Smith(1973)). In this paper, the properties of the $L_3(m)$ type PBIB designs are investigated. Extended Property A and fractional BNAS are defined and a solution formula for the treatment effects in the $L_32(m)$ type designs is obtained.

• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.601-610
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• 1999

Crossover design is officially except for special occasions recommended by KFDA and FDA for assessing Bioequivalence between two drugs one for reference and the other for innovator. Such design is regarded as a special case of latin square split-polt or repeated measurement design and its main difference with other designing methods is that each subject in an experiment is exposed two drugs in sequence. Therefore general statistical analysis is not suitable since the model for this experiment includes carryover effect in addition to period and sequence effect. in this paper analysis for crossover model with two drugs and its interpretation are mainly discussed and an example is given for illustration.