• 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.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2002.11a
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• pp.373-376
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• 2002

본 논문에서는 여러 가지 연산에 대해서 Hamming weight를 이용한 DPA 공격이 어떻게 가능하고, 그 결과는 어떠한가를 살펴본다. 각 연산에 대해서 먼저 1, 2차 DPA 공격이 어떻게 가능한지를 보인다. 각 연산 별로 얻어지는 결과들을 비교해 보고, 연산들이 DPA 공격에 대해 내부 정보를 얼마나 유출하며, 공격에 대해 안전한지를 알아본다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.7
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• pp.3455-3474
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• 2018

As a unique form of signed-digit representation, non-adjacent form (NAF) minimizes Hamming weight by removing a stream of non-zero bits from the binary representation of positive integer. Thanks to this strong point, NAF has been used in various applications such as cryptography, packet filtering and so on. In this paper, to improve the NAF conversion speed of the $NAF_w$ algorithm, we propose a new NAF conversion algorithm, called w-bit Shifting Non-Adjacent Form($SNAF_w$), where w is width of scanning window. By skipping some unnecessary bit comparisons, the proposed algorithm improves the NAF conversion speed of the $NAF_w$ algorithm. To verify the excellence of the $SNAF_w$ algorithm, the $NAF_w$ algorithm and the $SNAF_w$ algorithm are implemented in the 8-bit microprocessor ATmega128. By measuring CPU cycle counter for the NAF conversion under various input patterns, we show that the $SNAF_2$ algorithm not only increases the NAF conversion speed by 24% on average but also reduces deviation in the NAF conversion time for each input pattern by 36%, compared to the $NAF_2$ algorithm. In addition, we show that $SNAF_w$ algorithm is always faster than $NAF_w$ algorithm, regardless of the size of w.

• 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 applied mathematics & informatics
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• v.26 no.1_2
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• pp.107-120
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• 2008

There has been a recent growth of interest in codes with respect to a newly defined non-Hamming metric grown as the Rosenbloom-Tsfasman metric (RT, or $\rho$, in short). In this paper, the definitions of the Lee complete $\rho$ weight enumerator and the exact complete $\rho$ weight enumerator of a code over $M_n_\times_s(Z_4)$ are given, and the MacWilliams identities with respect to this RT metric for the two weight enumerators of a linear code over $M_n_\times_s(Z_4)$ are proven too. At last, we also prove that the MacWilliams identities for the Lee and exact complete $\rho$ weight enumerators of a linear code over $M_n_\times_s(Z_4)$ are the generalizations of the MacWilliams identities for the Lee and complete weight enumerators of the corresponding code over $Z_4$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.2011-2023
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• 2015

This paper determines the structures of one-homogeneous weight codes over finite chain rings and studies the algebraic properties of these codes. We present explicit constructions of one-homogeneous weight codes over finite chain rings. By taking advantage of the distance-preserving Gray map defined in [7] from the finite chain ring to its residue field, we obtain a family of optimal one-Hamming weight codes over the residue field. Further, we propose a generalized method that also includes the examples of optimal codes obtained by Shi et al. in [17].

• Journal of Communications and Networks
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• v.10 no.1
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• pp.5-9
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• 2008

Researchers have investigated many upper bound techniques applicable to error probabilities on the maximum likelihood (ML) decoding performance of turbo-like codes and low density parity check (LDPC) codes in recent years for a long codeword block size. This is because it is trivial for a short codeword block size. Previous research efforts, such as the simple bound technique [20] recently proposed, developed upper bounds for LDPC codes and turbo-like codes using ensemble codes or the uniformly interleaved assumption. This assumption bounds the performance averaged over all ensemble codes or all interleavers. Another previous research effort [21] obtained the upper bound of turbo-like code with a particular interleaver using a truncated union bound which requires information of the minimum Hamming distance and the number of codewords with the minimum Hamming distance. However, it gives the reliable bound only in the region of the error floor where the minimum Hamming distance is dominant, i.e., in the region of high signal-to-noise ratios. Therefore, currently an upper bound on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix cannot be calculated because of heavy complexity so that only average bounds for ensemble codes can be obtained using a uniform interleaver assumption. In this paper, we propose a new bound technique on ML decoding performance for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix using ML estimated weight distributions and we also show that the practical iterative decoding performance is approximately suboptimal in ML sense because the simulation performance of iterative decoding is worse than the proposed upper bound and no wonder, even worse than ML decoding performance. In order to show this point, we compare the simulation results with the proposed upper bound and previous bounds. The proposed bound technique is based on the simple bound with an approximate weight distribution including several exact smallest distance terms, not with the ensemble distribution or the uniform interleaver assumption. This technique also shows a tighter upper bound than any other previous bound techniques for turbo-like code with a particular interleaver and LDPC code with a particular parity check matrix.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.38 no.2
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• pp.51-51
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• 2001

본 논문은 디지털 순서회로 설계시 상태할당 알고리즘 개발에 관한 연구로, 동적 소비전력을 감소시키기 위하여 상태변수의 변화를 최소로 하는 코드를 할당하여 상태코드가 변화하는 스위칭횟수를 줄이도록 하였다. 상태를 할당하는데는 Markov의 확률함수를 이용하여 hamming거리가 최소가 되도록 상태 천이도에서 각 상태를 연결하는 edge에 weight를 정의한 다음, 가중치를 이용하여 각 상태들간의 연결성을 고려하여 인접한 상태들간에는 가능한 적은 비트 천이를 가지도륵 모든 상태를 반복적으로 찾아 계산하였다. 비트 천이의 정도를 나타내기 위하여 cost 함수로 계산한 결과 순서회로의 종류에 따라 Lakshmikant의 알고리즘보다 최고 57.42%를 감소시킬 수 있었다.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.38 no.2
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• pp.137-144
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• 2001

In this paper, a state assignment algorithm was proposed to reduce power consumption in control-flow oriented finite state machines. The Markov chain model is used to reduce the switching activities, which closely relate with dynamic power dissipation in VLSI circuits. Based on the Markov probabilistic description model of finite state machines, the hamming distance between the codes of neighbor states was minimized. To express the switching activities, the cost function, which also accounts for the structure of a machine, is used. The proposed state assignment algorithm is tested with Logic Synthesis Benchmarks, and reduced the cost up to 57.42% compared to the Lakshmikant's algorithm.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.37 no.6
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• pp.72-84
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• 2000

The test patterns for path delay faults consist of two patterns. So in order to test the delay faults, a new weight generation algorithm that is different from the weight generation algorithm for stuck-at faults must be applied. When deterministic test patterns for weight calculation are used, the deterministic test patterns must be divided into several subsets, so that Hamming distances between patterns are not too long. But this method makes the number of weight sets too large in delay testing, and may generate inaccurate weights. In this pater, we perform fault simulation without pattern partition. Experimental results for ISCAS 89 benchmark circuits prove the effectiveness of the new weight generation algorithm proposed in this paper.