• 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 KIISE:Computing Practices and Letters
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• v.16 no.6
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• pp.648-653
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• 2010

The non-metric multidimensional scaling (nMDS) is a method for analyzing the relation among objects by mapping them onto the Euclidean space. The nMDS is useful when it is difficult to use the concept of distance between pairs of objects due to non-metric dissimilarities between objects. The nMDS can be regarded as an optimization problem in which there are many local optima. Since the conventional nMDS algorithm utilizes the steepest descent method, it has a drawback in that the method can hardly find a better solution once it falls into a local optimum. To remedy this problem, in this paper, we applied the simulated annealing to the nMDS and proposed a new optimization algorithm which could search for a global optimum more effectively. We examined the algorithm using benchmarking problems and found that improvement rate of the proposed algorithm against the conventional algorithm ranged from 0.7% to 3.2%. In addition, the statistical hypothesis test also showed that the proposed algorithm outperformed the conventional one.

• Ocean and Polar Research
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• v.38 no.2
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• pp.115-128
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• 2016

This study examined the relationship between macrobenthic distribution patterns and environmental factors in salt marsh vegetation in Donggeomdo, Ganghwa on the west coast of Korea. Nine stations were fixed on a transect across the salt marsh vegetation, and field sampling was carried out monthly from July 1997 to June 1998. A total of 38 species of macrobenthos were recorded: each of faunal groups, 13 (34.2%) Arthropoda, 12 (31.6%) Polychaeta, 8 (21.1%) Mollusca, and 5 (13.2%) others. The mean density was $2,659individuals/m^2$, with a mean biomass of $178.6gWWt/m^2$. Mollusca dominated in terms of abundance and biomass, with a mean density of $2,172individuals/m^2$ (81.7%) and a mean biomass of $131.9gWWt/m^2$ (73.9%). The number of species decreased in winter (January-February), while mean density increased in the spring (May-June). The biomass was relatively in Summer and Fall (July-November), than any other season. The number of species was high in pure stands of Suaeda japonica in the lower salt marsh vegetation, and the mean density and biomass were high in mixed halophyte communities in the middle salt marsh vegetation. Two Mollusca, the bivalve Glauconome chinensis and gastropod Assiminea lutea, were dominant. The densities of these two species were high in mixed halophyte communities in the middle salt marsh vegetation. Non-metric multi-dimensional scaling (nMDS) showed that the study area could be divided into four groups corresponding to the vertical distribution of tidal levels and halophytes. Spearman's rank correlation revealed that the distribution patterns and community structure of macrobenthos were related to environment variables such as salinity of the substrates, exposure time, and grain size compositions of the sediment in the salt marsh vegetation. Particularly, the distribution and density of some dominant species showed differences along the vertical distributions of halophytes.