• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1037-1049
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• 2018

In this paper, we have first presented the construction of the linear characters of a finite Coxeter group $G_n$ of type $B_n$ by lifting all linear characters of the quotient group $G_n/[G_n,G_n]$ of the commutator subgroup $[G_n,G_n]$. Also we show that the sets of distinguished coset representatives $D_A$ and $D_{A^{\prime}}$ for any two signed compositions A, A' of n which are $G_n$-conjugate to each other and for each conjugate class ${\mathcal{C}}_{\lambda}$ of $G_n$, where ${\lambda}{\in}\mathcal{BP}(n)$, the equality ${\mid}{\mathcal{C}}_{\lambda}{\cap}D_A{\mid}={\mid}{\mathcal{C}}_{\lambda}{\cap}D_{A^{\prime}}{\mid}$ holds. Finally, we have given the general structure of units of Mantaci-Reutenauer algebra.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.823-833
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• 2009

It is well-known that if a convex hyperbolic polygon is constructed as a fundamental domain for a subgroup of the modular group, then its translates by the group elements form a locally finite tessellation and its side-pairing transformations form a system of generators for the group. Such hyperbolically convex polygons can be obtained by using Dirichlet's and Ford's polygon constructions. Another method of obtaining a fundamental domain for subgroups of the modular group is through the use of a right coset decomposition and we call such domains standard fundamental domains. In this paper we give subgroups of the modular group which do not have hyperbolically convex standard fundamental domain containing only inequivalent cusps.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.117-139
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• 2017

This paper presents a systematic study for theoretical aspects of a unified approach to the abstract relative Fourier transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor. Let H be a locally compact group, K be a locally compact Abelian (LCA) group, and ${\theta}:H{\rightarrow}Aut(K)$ be a continuous homomorphism. Let $G_{\theta}=H{\ltimes}_{\theta}K$ be the semi-direct product of H and K with respect to ${\theta}$ and $G_{\theta}/H$ be the canonical homogeneous space (left coset space) of $G_{\theta}$. We introduce the notions of relative dual homogeneous space and also abstract relative Fourier transform over $G_{\theta}/H$. Then we study theoretical properties of this approach.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.4C
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• pp.379-388
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• 2007

In this paper, we propose an adaptive turbo decoding algorithm for high order modulation scheme combined with originally design for a standard rate-1/2 turbo decoder for B/QPSK modulation. A transformation applied to the incoming I-channel and Q-channel symbols allows the use of an off-the-shelf B/QPSK turbo decoder without any modifications. Adaptive turbo decoder process the received symbols recursively to improve the performance. As the number of iterations increase, the execution time and power consumption also increase as well. The source of the latency and power consumption reduction is from the combination of the radix-4, dual-path processing, parallel decoding, and early-stop algorithms. We implemented the proposed scheme on a field-programmable gate array (FPGA) and compared its decoding speed with that of a conventional decoder. From the result of implementation, we confirm that the decoding speed of proposed adaptive decoding is faster than conventional scheme by 6.4 times.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.5
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• pp.646-655
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• 2012

First, we prove a number of results about interval-valued fuzzy groups involving the notions of interval-valued fuzzy cosets and interval-valued fuzzy normal subgroups which are analogs of important results from group theory. Also, we introduce analogs of some group-theoretic concepts such as characteristic subgroup, normalizer and abelian groups. Secondly, we prove that if A is an interval-valued fuzzy subgroup of a group G such that the index of A is the smallest prime dividing the order of G, then A is an interval-valued fuzzy normal subgroup. Finally, we show that there is a one-to-one correspondence the interval-valued fuzzy cosets of an interval-valued fuzzy subgroup A of a group G and the cosets of a certain subgroup H of G.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.369-388
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• 2005

First, we prove a number of results about intuitionistic fuzzy groups involving the notions of intuitionistic fuzzy cosets and intuitionistic fuzzy normal subgroups which are analogs of important results from group theory. Also, we introduce analogs of some group-theoretic concepts such as characteristic subgroup, normalizer and Abelian groups. Secondly, we prove that if A is an intuitionistic fuzzy subgroup of a group G such that the index of A is the smallest prime dividing the order of G, then A is an intuitionistic fuzzy normal subgroup. Finally, we show that there is a one-to-one correspondence the intuitionistic fuzzy cosets of an intuitionistic fuzzy subgroup A of a group G and the cosets of a certain subgroup H of G.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1327-1337
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• 2022

Zero-difference balanced (ZDB) functions can be applied to many areas like optimal constant composition codes, optimal frequency hopping sequences etc. Moreover, it has been shown that the image set of some ZDB functions is a regular partial difference set, and hence provides strongly regular graphs. Besides, perfect nonlinear functions are zero-difference balanced functions. However, the converse is not true in general. In this paper, we use the decomposition of cyclotomic polynomials into irreducible factors over 𝔽_p, where p is an odd prime to generalize some recent results on ZDB functions. Also we extend a result introduced by Claude et al. [3] regarding zero-difference-p-balanced functions over 𝔽_pⁿ. Eventually, we use these results to construct some optimal constant composition codes.

• ETRI Journal
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• v.29 no.3
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• pp.363-370
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• 2007

In this paper, we propose a flexible turbo decoding algorithm for a high order modulation scheme that uses a standard half-rate turbo decoder designed for binary quadrature phase-shift keying (B/QPSK) modulation. A transformation applied to the incoming I-channel and Q-channel symbols allows the use of an off-the-shelf B/QPSK turbo decoder without any modifications. Iterative codes such as turbo codes process the received symbols recursively to improve performance. As the number of iterations increases, the execution time and power consumption also increase. The proposed algorithm reduces the latency and power consumption by combination of the radix-4, dual-path processing, parallel decoding, and early-stop algorithms. We implement the proposed scheme on a field-programmable gate array and compare its decoding speed with that of a conventional decoder. The results show that the proposed flexible decoding algorithm is 6.4 times faster than the conventional scheme.

• East Asian mathematical journal
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• v.23 no.1
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• pp.23-36
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• 2007

In this paper we consider the fuzzy ideals of N-group G where N is a nearring. We introduce fuzzy ideal ${\theta}_{\mu}$ of the quotient N-group $G/{\mu}$ with respect to a fuzzy ideal $\mu$ of G. If $\mu$ is a fuzzy ideal of G and $\theta$ a fuzzy ideal of $G/{\mu}$ such that ${\theta}_{\mu}\;{\subseteq}\;{\theta}$ and ${\theta}_{\mu}(0)\;=\;{\theta}(0)$, then corresponding ${\sigma}_{\theta}\;:\;G\;{\rightarrow}\;[0,\;1]$ is defined and proved that it is a fuzzy ideal of G such that ${\mu}\;{\subseteq}\;{\sigma}_{\theta}$ and ${\mu}(0)\;=\;{\sigma}_{\theta}(0)$. We also prove some results on homomorphisms and fuzzy ideals of N-groups. The image and preimage of fuzzy ideal $\mu$ under N-group homomorphism were studied. Finally it is obtained that if $f\;:\;G\;{\rightarrow}\;G^1$ is an epimorphism of N-groups, then there is an order preserving bijection between the fuzzy ideals of $G^1$ and the fuzzy ideals of G that are constant on kerf. Some examples related to these concepts were illustrated.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.8C
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• pp.1069-1075
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• 2004

In this paper, we show the equivalence between complementary code keying (CCK) codeword and coset of the first order Reed-Muller (RM) code with variables of three. The CCK codewords are Golay sequences which have peak-to-average power ratio (PAPR) of two at most and can correct one error. We propose a CCK-orthogonal frequency division multiplexing (OFDM) modem to reduce PAPR. Also, we present the performance improvement techniques by increasing the variables of four to correct three errors and reduce PAPR at least 9㏈ with this system. Although, two Fast Hadamard Transform (FHT) blocks of size 8 64 are required at the receiver, we reduce the complexity by using FHT blocks of size 8 64 and 2 4 without deteriorating the performance. We generalize our results that we may increase the variables of RM code to enhance the error correcting and PAPR reduction capabilities without increasing receiver's complexity.