• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.7
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• pp.1315-1320
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• 2007

In this paper, we introduce a new fuzzy model called fuzzy combined polynomial neural networks, which are based on the representative fuzzy model named polynomial fuzzy model. In the design procedure of the proposed fuzzy model, the coefficients on consequent parts are estimated by using not general least square estimation algorithm that is a sort of global learning algorithm but weighted least square estimation algorithm, a sort of local learning algorithm. We are able to adopt various type of structures as the consequent part of fuzzy model when using a local learning algorithm. Among various structures, we select Polynomial Neural Networks which have nonlinear characteristic and the final result of which is a complex mathematical polynomial. The approximation ability of the proposed model can be improved using Polynomial Neural Networks as the consequent part.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.129-148
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• 1996

This paper propose the inference mechanism for handling linear polynomial constraints called consistency checking algorithm based on the feasibility checking algorithm borrowed from linear pro-gramming. in contrast with other approaches proposed algorithm can efficiently and coherented by linear polynomial forms. The developed algorithm is successfully applied to the symbolic simulation that offers a convenient means to conduct multiple simultaneous exploration of model behaviors.

• Journal of Integrative Natural Science
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• v.1 no.2
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• pp.149-159
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• 2008

We develop two algorithms that nd a minimal polynomial of a finite sequence. One uses Euclid's algorithm, and the other is in essence a minimal polynomial version of the Berlekamp-Massey algorithm. They are formulated naturally and proved algebraically using polynomial arithmetic. They connects up seamlessly with decoding procedure of alternant codes.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.30A no.11
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• pp.21-28
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• 1993

Decoding algorithm of noncyclic Reed-Solomon codes consists of four steps which are to compute syndromes, to find error-location polynomial, to decide error-location, and to solve error-values. There is a decoding method by which the computation of both error-location polynomial and error-evaluator polynimial can be avoided in conventional decoding methods using Euclid algorithm. The disadvantage of this method is that the same amount of computation is needed that is equivalent to solve the avoided polynomial. This paper considers the division method on polynomial on GF(2$^{m}$) systematically. And proposes a novel method to find error correcting polynomial by simple mathematical expression without the same amount of computation to find the two avoided polynomial. Especially. proposes the method which the amount of computation to find F (x) from the division M(x) by x, (x-1),....(x--${\alpha}^{n-2}$) respectively can be avoided. By applying the simple expression to decoding procedure on RS codes, propses a new decoding algorithm, and to show the validity of presented method, computer simulation is performed.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1285-1293
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• 2011

We establishes the polynomial convergence of a new class of path-following methods for semidefinite linear complementarity problems (SDLCP) whose search directions belong to the class of directions introduced by Monteiro [9]. Namely, we show that the polynomial iteration-complexity bound of the well known algorithms for linear programming, namely the predictor-corrector algorithm of Mizuno and Ye, carry over to the context of SDLCP.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.11 no.1
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• pp.35-42
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• 2001

The primitive polynomial on GF(q) is used in the area of the scrambler, the error correcting code and decode, the random generator and the cipher, etc. The algorithm that generates efficiently the primitive polynomial on GF(q) was proposed by A.D. Porto. The algorithm is a method that generates the sequence of the primitive polynomial by repeating to find another primitive polynomial with a known primitive polynomial. In this paper, we propose the algorithm that is improved in the A.D. Porto algorithm. The running rime of the A.D. Porto a1gorithm is O($\textrm{km}^2$), the running time of the improved algorithm is 0(m(m+k)). Here, k is gcd(k, $q^m$-1). When we find the primitive polynomial with m odor, it is efficient that we use the improved algorithm in the condition k, m>>1.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.40 no.6
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• pp.127-140
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• 2003

This paper develops a novel algorithm of computing 2 Dimensional Discrete Cosine Transform (2D-DCT) via Polynomial Transform (PT) converting 2D-DCT to the sum of 1D-DCTs. In computing N${\times}$M size 2D-DCT, the conventional row-column algorithm needs 3/2NMlog$_2$(NM)-2NM＋N＋M additions and 1/2NMlog$_2$(NM) additions and 1/2NMlog$_2$(NM) multiplications, while the proposed algorithm needs 3/2NMlog$_2$M＋NMlog$_2$N-M-N/2＋2 additions and 1/2NMlog$_2$M multiplications The previous polynomial transform needs complex operations because it applies the Euler equation to DCT. Since the suggested algorithm exploits the modular regularity embedded in DCT and directly decomposes 2D DCT into the sum of ID DCTs, the suggested algorithm does not require any complex operations.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.9 no.3
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• pp.3-12
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• 1999

The public key crytptosystem is represented by RSA based on the difficulty of integer factorization and ElGamal cryptosystem based on the intractability of the discrete logarithm problem in a cyclic group G. The index-calculus algorithm for discrete logarithms in GF${$q^n$}^+$ requires an polynomial factorization. The Niederreiter recently developed deterministic facorization algorithm for polynomial over GF$q^n$ In this paper we implemented the arithmetic of finite field with c-language and gibe an implementation of the Niederreiter's algorithm over GF$2^n$ using normal bases.

• Proceedings of the IEEK Conference
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• 2003.07c
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• pp.2617-2620
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• 2003

This paper presents the construction algorithm of the irreducible polynomial which needs to multiply over GF(2$\^$m/) and the flow chart representing the proposed algorithm has been proposed. And also, we get the degree from the value of xm＋k formation to the value of k = 7 using the proposed flow chart. The multiplier circuit has been implemented by using the proposed irreducible polynomial generation(IPG) algorithm in this paper, and we compared the proposed circuit with the conventional one. In the case of k = 7, one AND gate and five Ex-or gates are needed as the delay time for the irreducible polynomial in the proposed algorithm, but seven AND gates and sever Ex-or gates in the conventional one. As a result, the proposed algorithm shows the improved performance on the delay time.

• Convergence Security Journal
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• v.14 no.7
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• pp.59-64
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• 2014

We investigate $p(n){\cdot}2^{O(\sqrt{n})}$ algorithm for 0/1 knapsack problem where x is the total bit length of a list of sizes of n objects. The algorithm is adaptable of method that achieves a similar complexity for the partition and Subset Sum problem. The method can be applied to other optimization or decision problem based on a list of numerics sizes or weights. 0/1 knapsack problem can be used to solve NP-Complete Problems with pseudo-polynomial time algorithm. We try to apply this technique to bio-informatics problem which has pseudo-polynomial time complexity.