• East Asian mathematical journal
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• v.17 no.1
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• pp.167-174
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• 2001

We find the generalized Hamming weights of cyclic linear q-ary codes which are generated by a codeword of weight 2, and of any length.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.283-293
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• 2010

In this paper, inverse constrained minimum spanning tree problem under Hamming distance. Such an inverse problem is to modify the weights with bound constrains so that a given feasible solution becomes an optimal solution, and the deviation of the weights, measured by the weighted Hamming distance, is minimum. We present a strongly polynomial time algorithm to solve the inverse constrained minimum spanning tree problem under Hamming distance.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.10
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• pp.588-592
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• 2004

Scalar multiplication is to compute $textsc{k}$P when an integer $textsc{k}$ and an elliptic curve point f are given. As a general method to accelerate scalar multiplication, Agnew, Mullin and Vanstone proposed to use $textsc{k}$'s with fixed Hamming weights. We suggest a new method that uses $textsc{k}$'s with fixed signed Hamming weights and show that this method is more secure.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.2
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• pp.457-476
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• 2011

This paper presents an improved XOR-based Data Hiding Scheme (XDHS) to hide a halftone image in more than two halftone stego images. The hamming weight and hamming distance is a very important parameter affecting the quality of a halftone image. For this reason, we proposed a method that involves minimizing the hamming weights and hamming distances between the stego image and cover image in $2{\times}2$-pixel grids. Moreover, our XDHS adopts a block-wise operation to improve the quality of a halftone image and stego images. Furthermore, our scheme improves security by using a block-wise operation with A-patterns and B-patterns. Our XDHS method achieves a high quality with good security compared to the prior arts. An experiment verified the superiority of our XDHS compared with previous methods.

• Proceedings of the Optical Society of Korea Conference
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• 2001.02a
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• pp.64-65
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• 2001

HDDS(Holographic Digital Data Storage) 시스템에서 저장밀도가 증가함에 따라서 기록/재생된 데이터는 중첩된 페이지 사이의 간섭과 인접 픽셀간의 간섭에서 기인하는 ISI (Intersymbol Interference) 및 Speckle 잡음을 포함하는 Random Noise와 광학 수차, 광학정렬 오차 및 Laser 광원의 비균일 광강도 분포 등에서 기인하는 Non- random Noise 등 다양한 시스템 잡음에 의해서 BER 이 급격히 저하되는 문제가 발생된다. 113 이러한 문제점을 해소하고 시스템의 기록/재생 데이터 신뢰도를 확보하기 위해서는 적절한 광신호처리 기법과 coding 기법이 도입되어야만 한다. (중략)

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1996.11a
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• pp.286-294
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• 1996

In a remarkable paper 〔3〕, Hammons et al. showed that, when properly defined, the binary nonlinear Preparata code can be considered as the Gray map of a linear code eve. Z$_4$, the so-called Preparata code eve. Z$_4$. Recently, Yang and Helleseth 〔12〕 considered the generalized Hamming weights d$\_$r/(m) for Preparata codes of length 2$\^$m/ over Z$_4$ and exactly determined d$\_$r/, for r = 0.5,1.0,1.5,2,2.5 and 3.0. In particular, they completely determined d$\_$r/(m) for any r in the case of m $\leq$ 6. In this paper we show that the Preparata code of length 16 over Z$_4$ does not satisfy the chain condition.

• 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.

• East Asian mathematical journal
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• v.12 no.2
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• pp.155-162
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• 1996

• East Asian mathematical journal
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• v.12 no.2
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• pp.147-153
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• 1996

• Journal of the Korea Institute of Information Security & Cryptology
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• v.19 no.2
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• pp.23-30
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• 2009

Recently, rotation symmetric Boolean functions have attracted attention since they are suitable for fast evaluation and show good cryptographic properties. For example, important problems in coding theory were settled by searching the desired functions in the rotation symmetric function space. Moreover, they are applied to designing fast hashing algorithms. On the other hand, for some homogeneous rotation symmetric quadratic functions of simple structure, the exact formulas for their Hamming weights and nonlinearity were found[2,8]. Very recently, more formulations were carried out for much broader class of the functions[6]. In this paper, we make a further improvement by deriving the formula for the Hamming weight of quadratic rotation symmetric functions containing linear terms.