• 충청수학회지
• /
• 제33권2호
• /
• pp.255-270
• /
• 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
• /
• 제4권3_4호
• /
• pp.211-219
• /
• 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.

• 충청수학회지
• /
• 제36권3호
• /
• pp.181-194
• /
• 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.

• 한국정보통신학회논문지
• /
• 제7권7호
• /
• pp.1462-1470
• /
• 2003

정보통신의 발달과 인터넷의 확산으로 인해 정보보안의 필요성이 증대되면서 다양한 암호알고리즘이 개발되어 활용되고 있다. 이와 더불어 암호 공격 기술도 발전하여서, 공격에 강한 알고리즘에 대한 연구가 활발하게 진행되고 있다. Substitution Permutation Networks(SPN)등의 블록 암호알고리즘에서 교환계층의 선형변환행렬이 Maximum Distance Separable(MDS) 코드를 생성하면 차분공격과 선형공격에 강한 특성을 보인다. 본 논문에서는 선형변환행렬이 MDS 코드를 생성하는가를 판단하는 새로운 알고리즘을 제안한다. 선행변환행렬의 입력코드는 GF(2$^n$)상의 원소들로 이들을 변수로 해석할 수 있다. 하나의 변수를 다른 변수들의 대수식으로 변환하고 대입하여 변수를 하나씩 소거한다. 변수가 하나이고 모든 계수가 ‘0’이 아니면 선형변환 행렬은 MDS 코드를 생성한다. 본 논문에서 제안한 알고리즘은 기존의 모든 정방부분행렬이 정칙인지를 판단하는 알고리즘과 비교하여 곱셈 및 역수 연산수를 많이 줄임으로서 수행 시간을 크게 감소 시켰다.

• Journal of Communications and Networks
• /
• 제13권4호
• /
• pp.393-399
• /
• 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
• /
• 제30권5_6호
• /
• pp.821-827
• /
• 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
• /
• 제13권4호
• /
• pp.397-407
• /
• 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
• /
• 제9권2호
• /
• pp.129-131
• /
• 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 $i$.

• 대한수학회지
• /
• 제47권6호
• /
• pp.1167-1182
• /
• 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.

• 대한수학회보
• /
• 제59권6호
• /
• pp.1557-1565
• /
• 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.