• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.10
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• pp.5058-5077
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• 2019

Traditional regenerating codes are designed to tolerate node failures with optimal bandwidth overhead. However, there are many types of partial failures inside the node, such as latent sector failures. Recently, proposed regenerating codes can also repair intra-node failures with node-level redundancy but incur significant bandwidth and I/O overhead. In this paper, we construct a new scheme of regenerating codes, called IR-RBT codes, which employs intra-node redundancy to tolerate intra-node failures and serve as the help data for other nodes during the repair operation. We propose 2 algorithms for assigning the intra-node redundancy and RBT-Helpers according to the failure probability of each node, which can flexibly adjust the helping relationship between nodes to address changes in the actual situation. We demonstrate that the IR-RBT codes improve the bandwidth and I/O efficiency during intra-node failure repair over traditional regenerating codes but sacrifice the storage efficiency.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.725-742
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• 2014

In this paper, we find all inequivalent classes of self-orthogonal codes over $Z_{p^2}$ of lengths $l{\leq}3$ for all primes p, using similar method as in [3]. We find that the classification of self-orthogonal codes over $Z_{p^2}$ includes the classification of all codes over $Z_p$. Consequently, we classify all the codes over $Z_p$ and self-orthogonal codes over $Z_{p^2}$ of lengths $l{\leq}3$ according to the automorphism group of each code.

• Korean Journal of Mathematics
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• v.15 no.1
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• pp.79-85
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• 2007

We study codes over the polynomial ring $\mathbb{F}_q[D]$ and introduce the notion of basic codes which play a fundamental role in the theory.

• Journal of Communications and Networks
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• v.17 no.4
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• pp.351-361
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• 2015

In this paper, a new decoding scheme is proposed to improve the error correcting performance of low-density parity-check (LDPC) codes in high signal-to-noise ratio (SNR) region by using post-processing. It behaves as follows: First, a conventional LDPC decoding is applied to received LDPC codewords one by one. Then, we count the number of word errors in a predetermined number of decoded codewords. If there is no word error, nothing needs to be done and we can move to the next group of codewords with no delay. Otherwise, we perform a proper post-processing which produces a new soft-valued codeword (this will be fully explained in the main body of this paper) and then apply the conventional LDPC decoding to it again to recover the unsuccessfully decoded codewords. For the proposed decoding scheme, we adopt a simple product code structure which contains LDPC codes and simple algebraic codes as its horizontal and vertical codes, respectively. The decoding capability of the proposed decoding scheme is defined and analyzed using the parity-check matrices of vertical codes and, especially, the combined-decodability is derived for the case of single parity-check (SPC) codes and Hamming codes used as vertical codes. It is also shown that the proposed decoding scheme achieves much better error correcting capability in high SNR region with little additional decoding complexity, compared with the conventional LDPC decoding scheme.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.43-56
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• 2020

Recently, linear codes constructed from defining sets have been studied widely and determined their complete weight enumerators and weight enumerators. In this paper, we obtain complete weight enumerators of linear codes and weight enumerators of linear codes. These codes have at most three weight linear codes. As application, we show that these codes can be used in secret sharing schemes and authentication codes.

• Korean Journal of Mathematics
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• v.11 no.1
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• pp.57-64
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• 2003

We define $Z_16$ quadratic residue codes in term of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties of quadratic residue codes over a field.

• Journal of Broadcast Engineering
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• v.8 no.4
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• pp.437-451
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• 2003

With the rapid growth of internet technologies and wide availability of multimedia computing facilities, the enforcement of multimedia copyright protection becomes an important issue. Digital watermarking is viewed as an effective way to deter content users from illegal distributions. In recent years, digital watermarking has been intensively studied to achieve this goal. However, when the watermarked media is transmitted over the channels modeled as the additive white Gaussian noise (AWGN) channel, the watermark information is often interfered by the channel noise and produces a large number of errors. So many error-correcting codes have been applied in the digital watermarking system to protect the embedded message from the disturbance of the noise, such as BCH codes, Reef-Solomon (RS) codes and Turbo codes. Recently, low-density parity-check (LDPC) codes were demonstrated as good error correcting codes achieving near Shannon limit performance and outperforming turbo codes nth low decoding complexity. In this paper, in order to mitigate the channel conditions and improve the quality of watermark, we proposed the application of LDPC codes on implementing a fairly robust digital image watermarking system. The implemented watermarking system operates in the spectrum domain where a subset of the discrete wavelet transform (DWT) coefficients is modified by the watermark without using original image during watermark extraction. The quality of watermark is evaluated by taking Into account the trade-off between the chip-rate and the rate of LDPC codes. Many simulation results are presented in this paper, these results indicate that the quality of the watermark is improved greatly and the proposed system based on LDPC codes is very robust to attacks.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.103-112
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• 2005

Using the Newton's identities, we give the inductive formula for the generator polynomials of the $p$-adic quadratic residue codes.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.751-764
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• 2016

We investigate the self-dual codes over Galois rings and determine the mass formula for self-dual codes over Galois rings $GR(p^2,2)$.

• Journal of Fashion Business
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• v.26 no.6
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• pp.1-13
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• 2022

The purpose of this study was to find out the type of fashion codes hip-hop fashion has in contemporary Chinese fashion, and the frequency and characteristics of each fashion code. Text mining, which is the most basic analysis method in big data analyticswas used rather than traditional design element analysis. Specific results were as follows. First, hip-hop initially entered China in the late 1970s. The most historical turning point was the American film "Breakin". Second, frequency and word cloud analysis results showed that the "national tide" fashion code was the most notable code. Third, through word embedding analysis, fashion codes were divided into types of "original hip-hop codes", "trendy hip-hop codes", and "hip-hop codes grafted with traditional Chinese culture".