• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.255-270
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• 2020

We studied the MDS self-dual codes over finite chain rings. We stated the projection and lifting of codes over the finite chain rings with respect to the MDS self-dual codes, and then we applied the results to the MDS self-dual codes over Galois rings.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.211-219
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• 2022

We study MDS(maximum distance separable) self-dual codes over Galois ring R = GR(2^m, r). We prove that there exists an MDS self-dual code over R of length n if (n - 1) divides (2^r - 1), and 2^m divides n. We also provide the current state of the problem for the existence of MDS self-dual codes over Galois rings.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.3
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• pp.181-194
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• 2023

Let GR(2^m, r) be a Galois ring with even characteristic. We are interested in the existence of MDS(Maximum Distance Separable) self-dual codes over GR(2^m, r). In this paper, we prove that there exists an MDS self-dual code over GR(2^m, r) with parameters [n, n/2, n/2 + 1] if (n - 1) | (2^r - 1) and 8 | n.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.7
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• pp.1462-1470
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• 2003

According to the necessity about information security as well as the advance of IT system and the spread of the Internet, a variety of cryptography algorithms are being developed and put to practical use. In addition the technique about cryptography attack also is advanced, and the algorithms which are strong against its attack are being studied. If the linear transformation matrix in the block cipher algorithm such as Substitution Permutation Networks(SPN) produces the Maximum Distance Separable(MDS) code, it has strong characteristics against the differential attack and linear attack. In this paper, we propose a new algorithm which cm estimate that the linear transformation matrix produces the MDS code. The elements of input code of linear transformation matrix over GF$({2_n})$ can be interpreted as variables. One of variables is transformed as an algebraic formula with the other variables, with applying the formula to the matrix the variables are eliminated one by one. If the number of variables is 1 and the all of coefficient of variable is non zero, then the linear transformation matrix produces the MDS code. The proposed algorithm reduces the calculation time greatly by diminishing the number of multiply and reciprocal operation compared with the conventional algorithm which is designed to know whether the every square submatrix is nonsingular.

• Journal of Communications and Networks
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• v.13 no.4
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• pp.393-399
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• 2011

We evaluate the link-level performance of cooperative multi-hop relaying networks with an maximum distance separable (MDS) code. The effect of the code on the link-level performance at the destination is investigated in terms of the outage probability and the spectral efficiency. Assuming a simple topology, we construct an absorbing Markov chain. Numerical results indicate that significant improvement can be achieved by incorporating an MDS code. MDS codes successfully facilitate recovery of the message block at a relaying node due to powerful error-correcting capability, so that it can reduce the outage probability. Furthermore, we evaluate the average number of hops where the message block can be delivered.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.821-827
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• 2012

In this paper, we prove that for all odd prime powers $q$ there exist MDS(maximum distance separable) self-dual codes over $\mathbb{F}_{q^2}$ for all even lengths up to $q+1$. Additionally, we prove that there exist MDS self-dual codes of length four over $\mathbb{F}_q$ for all $q$ > 2, $q{\neq}5$.

• Earthquakes and Structures
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• v.13 no.4
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• pp.397-407
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• 2017

With the growing demand for metallic dampers in engineering practice, it is urgent to establish a reasonable approach to evaluating the mechanical performance of metallic dampers under seismic excitations. This paper introduces an effective method for parameter identification of the modified Bouc-Wen model and its application to evaluating the fatigue performance of metallic dampers (MDs). The modified Bouc-Wen model which eliminates the redundant parameter is used to describe the hysteresis behavior of MDs. Relations between the parameters of the modified Bouc-Wen model and the mechanical performance parameters of MDs are studied first. A modified Genetic Algorithm using real-integer hybrid coding with relative fitness as well as adaptive crossover and mutation rates (called RFAGA) is then proposed to identify the parameters of the modified Bouc-Wen model. A reliable approach to evaluating the fatigue performance of the MDs with respect to the Chinese Code for Seismic Design of Buildings (GB 50011-2010) is finally proposed based on the research results. Experimental data are employed to demonstrate the process and verify the effectiveness of the proposed approach. It is shown that the RFAGA is able to converge quickly in the identification process, and the simulation curves based on the identification results fit well with the experimental hysteresis curves. Furthermore, the proposed approach is shown to be a useful tool for evaluating the fatigue performance of MDs with respect to the Chinese Code for Seismic Design of Buildings (GB 50011-2010).

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.129-131
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• 2001

Let $q=p^{e1}_1{\cdots}p^{em}_m$ be the product of distinct prime elements. In this short paper, we show that the largest value of M such that there exists an ($n$, M, $n-1$) $q$-ary code is $q^2$ if $n-1{\leq}p^{ei}_i$ for all $i$.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1167-1182
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• 2010

We study codes meeting a generalized version of the Singleton bound for higher weights. We show that some of the higher weight enumerators of these codes are uniquely determined. We give the higher weight enumerators for MDS codes, the Simplex codes, the Hamming codes, the first order Reed-Muller codes and their dual codes. For the putative [72, 36, 16] code we find the i-th higher weight enumerators for i = 12 to 36. Additionally, we give a version of the generalized Singleton bound for non-linear codes.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1557-1565
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• 2022

In this paper, Glift codes, generalized lifted polynomials, matrices are introduced. The advantage of Glift code is "distance preserving" over the ring R. Then optimal codes can be obtained over the rings by using Glift codes and lifted polynomials. Zero divisors are classified to satisfy "distance preserving" for codes over non-chain rings. Moreover, Glift codes apply on MDS codes and MDS codes are obtained over the ring 𝓡 and the non-chain ring 𝓡_e,s.