• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.83-116
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• 2020

Let G be a finite group. By a sequence over G, we mean a finite unordered sequence of terms from G, where repetition is allowed, and we say that it is a product-one sequence if its terms can be ordered such that their product equals the identity element of G. The large Davenport constant D(G) is the maximal length of a minimal product-one sequence, that is, a product-one sequence which cannot be factored into two non-trivial product-one subsequences. We provide explicit characterizations of all minimal product-one sequences of length D(G) over dihedral and dicyclic groups. Based on these characterizations we study the unions of sets of lengths of the monoid of product-one sequences over these groups.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.7
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• pp.1401-1410
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• 2017

Cryptographic synchronization which synchronizes internal state of cryptographic algorithm and ciphertext stream between an encryptor and a decryptor affects the quality of secure communication. If there happens a synchronization loss between a transmitter and a receiver in a secure communication, the output of the receiver is unintelligible until resynchronization is made. Especially, in the secure communication on a wireless channel with high BER, synchronization performance can dominate its quality. In this paper, we proposed a novel and noise robust synchronization signal generation method as well as its detection algorithm. We generated a synchronization signal in the form of a masking structure based on the maximal length sequence, and developed a detection algorithm using a correlation property of the maximal length sequence. Experimental results have demonstrated that the proposed synchronization signal outperforms the conventional concatenated type synchronization signal in a noisy environment.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.903-911
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• 2012

Let $\{u(t)\}$ and $\{u(dt)\}$ be two maximal length sequences of period $2^n-1$. The cross-correlation is defined by $C_d({\tau})=\sum{_{t=0}^{2^n-2}}(-1)^{u(t+{\tau})+v(t)$ for ${\tau}=0,1,{\cdots},2^n-2$. In this paper, we propose a new proof for finding the values and the number of occurrences of each value of $C_d({\tau})$ when $d=2^{k-2}(2^k+3)$, where $n=2k$, $k$ is a positive integer.

• International Journal of Contents
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• v.3 no.2
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• pp.18-24
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• 2007

Biological sequences such as DNA and amino acid sequences typically contain a large number of items. They have contiguous sequences that ordinarily consist of more than hundreds of frequent items. In biological sequences analysis(BSA), a frequent contiguous sequence search is one of the most important operations. Many studies have been done for mining sequential patterns efficiently. Most of the existing methods for mining sequential patterns are based on the Apriori algorithm. In particular, the prefixSpan algorithm is one of the most efficient sequential pattern mining schemes based on the Apriori algorithm. However, since the algorithm expands the sequential patterns from frequent patterns with length-1, it is not suitable for biological datasets with long frequent contiguous sequences. In recent years, the MacosVSpan algorithm was proposed based on the idea of the prefixSpan algorithm to significantly reduce its recursive process. However, the algorithm is still inefficient for mining frequent contiguous sequences from long biological data sequences. In this paper, we propose an efficient method to mine maximal frequent contiguous sequences in large biological data sequences by constructing the spanning tree with a fixed length. To verify the superiority of the proposed method, we perform experiments in various environments. The experiments show that the proposed method is much more efficient than MacosVSpan in terms of retrieval performance.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.957-964
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• 2014

In this paper, we prove that there is no branch point in the Lorentz space (M, d) which is the limit space of a sequence {($M_{\alpha},d_{\alpha}$)} of compact globally hyperbolic interpolating spacetimes with $C^{\pm}_{\alpha}$-properties and curvature bounded below. Using this, we also obtain that every maximal timelike geodesic in the limit space (M, d) can be expressed as the limit curve of a sequence of maximal timelike geodesics in {($M_{\alpha},d_{\alpha}$)}. Finally, we show that the limit space (M, d) satisfies a timelike triangle comparison property which is analogous to the case of Alexandrov curvature bounds in length spaces.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.15 no.5
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• pp.451-460
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• 2004

The pilot bit pattern of W-CDMA system is used for the channel estimation and frame synchronization confirmation. This paper proposes the binary sequences for the frame synchronization for wideband code division multiple access (W-CDMA) system. We present the circuit for the generation of ideal frame synchronization property using the binary sequences called frame synchronization word(FSW). W-CDMA system uses compressed mode where up to 7 slots per one 10 msec frame are not transmitted to make measurements from another frequency without a full dual receiver terminal. It is shown that the proposed frame synchronization words also maintain the optimal frame synchronization property in the compressed mode by using the complementary mapping relationship of preferred pair. And we discuss the realization circuit for the generation of frame synchronization words by using the concept of preferred pairs, complementary mapping relationship, and maximal length sequence.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.12
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• pp.1742-1744
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• 2016

In this letter, we prove equivalence of the Binary perturbation and Afterburner LDPC decoder that are proposed for improving the decoding performance in short length LDPC codes.

• The KIPS Transactions:PartD
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• v.15D no.2
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• pp.155-162
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• 2008

Biological sequences such as DNA sequences and amino acid sequences typically contain a large number of items. They have contiguous sequences that ordinarily consist of hundreds of frequent items. In biological sequences analysis(BSA), a frequent contiguous sequence search is one of the most important operations. Many studies have been done for mining sequential patterns efficiently. Most of the existing methods for mining sequential patterns are based on the Apriori algorithm. In particular, the prefixSpan algorithm is one of the most efficient sequential pattern mining schemes based on the Apriori algorithm. However, since the algorithm expands the sequential patterns from frequent patterns with length-1, it is not suitable for biological dataset with long frequent contiguous sequences. In recent years, the MacosVSpan algorithm was proposed based on the idea of the prefixSpan algorithm to significantly reduce its recursive process. However, the algorithm is still inefficient for mining frequent contiguous sequences from long biological data sequences. In this paper, we propose an efficient method to mine maximal frequent contiguous sequences in large biological data sequences by constructing the spanning tree with the fixed length. To verify the superiority of the proposed method, we perform experiments in various environments. As the result, the experiments show that the proposed method is much more efficient than MacosVSpan in terms of retrieval performance.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.21 no.5
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• pp.84-92
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• 2020

This paper describes the estimation method of cable fault location in rocket motors using M-sequence (Maximal Length Sequence). In order to estimate the location of a cable fault, three methods have been usually used: TDR (Time Domain Reflectometry), FDR (Frequency Domain Reflectometry), and TFDR (Time-Frequency Domain Reflectometry). However, these methods suffer the disadvantage of requiring users to be close to a test field, which is dangerous. The estimation method of cable fault location using M-sequence is proposed to solve this problem. The proposed method can make use of DAS (Data Acquisition System). The experiments were three cases: damaged, open, and short. The RG-58 coaxial cable was used in the experiments. As a result, the proposed method has better performance than that of conventional methods such as TDR and TFDR.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.817-826
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• 2015

Let R be a commutative ring with total quotient ring K. Each monomorphic R-module endomorphism of a cyclic R-module is an isomorphism if and only if R has Krull dimension 0. Each monomorphic R-module endomorphism of R is an isomorphism if and only if R = K. We say that R has property (${\star}$) if for each nonzero element $a{\in}R$, each monomorphic R-module endomorphism of R/Ra is an isomorphism. If R has property (${\star}$), then each nonzero principal prime ideal of R is a maximal ideal, but the converse is false, even for integral domains of Krull dimension 2. An integral domain R has property (${\star}$) if and only if R has no R-sequence of length 2; the "if" assertion fails in general for non-domain rings R. Each treed domain has property (${\star}$), but the converse is false.