• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.8
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• pp.1774-1779
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• 2005

This paper propose the design method of the constructing the digital logic systems over galois fields using by the galois field decision diagram(GFDD) that is based on the graph theory. The proposed design method is as following. First of all, we discuss the mathematical properties of the galois fields and the basic properties of the graph theory. After we discuss the operational domain and the functional domain, we obtain the transformation matrixes, $\psi$GF(P)(1) and $\xi$GF(P)(1), in the case of one variable, that easily manipulate the relationship between two domains. And we extend above transformation matrixes to n-variable case, we obtain $\psi$GF(P)(1) and $\xi$GF(P)(1). We discuss the Reed-Muller expansion in order to obtain the digital switching functions of the P-valued single variable. And for the purpose of the extend above Reed-Muller expansion to more two variables, we describe the Kronecker product arithmetic operation.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.807-810
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• 1998

This paper propose the method to produce GRM(Generalized Reed-Muller)expansion. The general method to obtain GRM expansion coefficient for p valued n variable is derivation of single variable transform matrix and expand it n times using Kronecker product. In this case the size of matrix increases depending on the augmentation of variables. In this paper we propose the simple algorithm to produce GRM coefficient using a single variable transform matrix.

• Proceedings of the IEEK Conference
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• 1999.06a
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• pp.745-748
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• 1999

This paper propose the method to derive RM(Reed-Muller) expansion coefficients for Multiple-Valued function. The general method to obtain RM expansion coefficient for p valued n variable is derivation of single variable transform matrix and expand it n times using Kronecker product. The transform matrix used is p$^{n}$ $\times$ p$^{n}$ matrix. In this case the size of matrix increases depending on the augmentation of variables and the operation is complicated. Thus, to solving the problem, we propose derivation of RM expansion coefficients using p$\times$p transform matrix and Karnaugh-map.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.1
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• pp.57-63
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• 1994

The logic function synthesis using ULM U$_h$ is constructed based on canonic Reed-Muller expansion coefficient for a given function. This paper proposes the fast synthesis algorithm using ULM U$_h$ for ternary function. By using circuit cost and synthesis method of proposed in this paper, order of control input variable minimum number of ULM U$_h$ can be decided in the synthesis of n-variable ternary function. Accordingly, this method enables to optimum circuit realization for ternary function synthesis using ULM ULM U$_h$ and can be applied to ternary function synthesis using ULM U$_h$. The complexity of search for select the order of all control input variables is (n+2)(n-1)/2.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.42 no.10 s.340
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• pp.17-24
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• 2005

This paper propose a new generation method of GRM coefficients using the circulation property of polarity over GF(3). The general method to derive GRM coefficients are obtain the filled polarity of GRM coefficients using RM expansion and expand it for the polarities. Since the general method has many operations when the number of the variables are incremented. Proposed method in this paper simplifies the generation procedure and reduces a number of operators compare to parallel type because of the cyclic property of polarity. Comparing to the proposed papers, the proposed method use only adders without multiplier. So it improves the complexity of the system with efficient composition of the circuits.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.36C no.5
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• pp.67-75
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• 1999

This paper presents a production method to GRM coefficients which are consist of $P^n$ polarities to n variables over GF(p). In general production method to GRM coefficients is derived from RM coefficients to polarity 0 using RM expansion and extended to GRM coefficients. The procedure of proposed production method to GRM coefficients is consists of 2 steps. First, obtain the optimal polarity which is contains a minimal operation to single variable and then apply the same process to all generation process of GRM coefficients using cyclic property of the polarity. Proposed method simplify the generation procedure and reduces a number of operators because of the cyclic property of polarity.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.4
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• pp.863-868
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• 2013

In recently years, many digital logic systems based on graph theory are analyzed and synthesized. This paper presented a method of constructing the function using edge valued extension graph which is based on graph theory. The graph is applied to a new data structure. from binary graph which is recently used in constructing the digital logic systems based on the graph theory. We discuss the mathematical background of literal and reed-muller expansion, and we discuss the edge valued extension graph which is the key of this paper. Also, we propose the algorithms which is the function derivation based on the proposed edge valued extension graph. That is the function minimization method of the n-variables m-valued functions and showed that the algorithm had the regularity with module by which the same blocks were made concerning about the schematic property of the proposed algorithm.