• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.2
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• pp.156-163
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• 2013

The use of an error-correcting code is essential in communication systems where the channel is noisy. When channel coding parameters are unknown at a receiver side, decoding becomes difficult. To perform decoding without the channel coding information, we should estimate the parameters. In this paper, we introduce a method to reconstruct the generator polynomial of BCH(Bose-Chaudhuri-Hocquenghem) codes based on the idea that the generator polynomial is compose of minimal polynomials and BCH code is cyclic code. We present a probability compensation method to improve the reconstruction performance. This is based on the concept that a random data pattern can also be divisible by a minimal polynomial of the generator polynomial. And we confirm the performance improvement through an intensive computer simulation.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.7
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• pp.1209-1217
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• 2008

In this paper, we present a new bit-parallel multiplier for performing the bit-parallel multiplication of two polynomials in the finite fields $GF(2^m)$. Prior to construct the multiplier circuits, we consist of the vector code generator(VCG) to generate the result of bit-parallel multiplication with one coefficient of a multiplicative polynomial after performing the parallel multiplication of a multiplicand polynomial with a irreducible polynomial. The basic cells of VCG have two AND gates and two XOR gates. Using these VCG, we can obtain the multiplication results performing the bit-parallel multiplication of two polynomials. Extending this process, we show the design of the generalized circuits for degree m and a simple example of constructing the multiplier circuit over finite fields $GF(2^4)$. Also, the presented multiplier is simulated by PSpice. The multiplier presented in this paper use the VCGs with the basic cells repeatedly, and is easy to extend the multiplication of two polynomials in the finite fields with very large degree m, and is suitable to VLSI.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.4
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• pp.505-514
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• 2015

This paper proposes a probabilistic generation assessment model of renewable energy generators(REGs) considering uncertainty of resources, mainly focused on Wind Turbine Generator(WTG) and Solar Cell Generator(SCG) which are dispersed widely in South Korea The proposed numerical analysis method assesses the one day-ahead generation by combining equivalent generation characteristics function and probabilistic distribution function of wind speed(WS) and solar radiation(SR) resources. The equivalent generation functions(EGFs) of the wind and solar farms are established by grouping a lot of the farms appropriately centered on Weather Measurement Station(WMS). First, the EGFs are assessed by using regression analysis method based on typical least square method from the recorded actual generation data and historical resources(WS and SR). Second, the generation of the REGs is assessed by adding the one day-ahead resources forecast, announced by WMS, to the EGFs which are formulated as third order degree polynomials using the regression analysis. Third, a Renewable Energy Generation Assessment System(REGAS) including D/B of recorded actual generation data and historical resources is developed using the model and algorithm predicting one day-ahead power output of renewable energy generators.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.789-830
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• 2003

By forming completions of families of noncommutative polynomials, we define a notion of noncommutative continuous function and locally bounded Borel function that give a noncommutative analogue of the functional calculus for elements of commutative $C^{*}$-algebras and von Neumann algebras. These notions give a precise meaning to $C^{*}$-algebras defined by generator and relations and we show how they relate to many parts of operator and operator algebra theory.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.459-479
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• 2020

In the last two decades, codes over noncommutative rings have been one of the main trends in coding theory. Due to the fact that noncommutativity brings many challenging problems in its nature, still there are many open problems to be addressed. In 2015, generator polynomial matrices and parity-check polynomial matrices of generalized quasi-cyclic (GQC) codes were investigated by Matsui. We extended these results to the noncommutative case. Exploring the dual structures of skew constacyclic codes, we present a direct way of obtaining parity-check polynomials of skew multi-twisted codes in terms of their generators. Further, we lay out the algebraic structures of skew multipolycyclic codes and their duals and we give some examples to illustrate the theorems.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.365-374
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• 2013

Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$, where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$. Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$. Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.819-821
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• 1998

This paper deals with a method or a residual generation for fault isolation in a centrifugal pump with a water circulation system, driven by a speed controlled dc motor. It is based on parity relations derived from the moving-average model of the system and is used to identify sensor faults and two possible brush and impeller faults, where the former is dealt with additive faults, while the latter characterized as discrepancies between the nominal and actual plant parameters of the system is modelled by multiplicative faults. We will represent the propagation of this uncertainty to the model matrices by the approximate handling of partial derivatives of polynomials. With multiplicative faults, the transformation matrix implemented in the residual generator are calculated on-line. The simulation studies demonstrate that small changes of the system can be detected and diagnosed by using the method.

• Journal of the Institute of Convergence Signal Processing
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• v.13 no.4
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• pp.194-200
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• 2012

In this paper we analyze the code sequence generating algorism defined on $GF(2^n)$ proposed by S.Bostas and V.Kumar[7] and derive the implementation functions of code sequence generator using Boolean functions which can map the vector space $F_2^n$ of all binary vectors of length n, to the finite field with two elements $F_2$. We find the code sequence generating boolean functions based on two kinds of the primitive polynomials of degree, n=5 and n=7 from trace function. We then design and implement the code sequence generators using these functions, and produce two code sequence groups. The two groups have the period 31 and 127 and the magnitudes of out of phase(${\tau}{\neq}0$) autocorrelation and crosscorrelation functions {-9, -1, 7} and {-17, -1, 15}, satisfying the period $L=2^n-1$ and the correlation functions $R_{ij}({\tau})=\{-2^{(n+1)/2}-1,-1,2^{(n+l)/2}-1\}$ respectively. Through these results, we confirm that the code sequence generators using boolean functions are designed and implemented correctly.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.36C no.1
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• pp.1-11
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• 1999

In this paper, we proposed a design method of parameterized viterbi decoder, which automatically synthsizes the diverse viterbi deciders used in the digital mobile communication systems. It is designed to synthesize a viterbi decoder specified by user-provided parameters. Those parameters are constraint length, code rate generator polynomials of teh convolutional encoder, data rate and bits/frame of the data transmission, and soft decision bits of viterbi decoder. For the design of the parameterized viterbi decoder, we designed a user interface module C-language, and a viterbi decoder module in a hierarchical atructure using VHDL language and its generic statement. For the verification of the parameterized viterbi decoder, we compared our synthesized viterbi decoder with the conventional viterbi decoder which is designed for the IS-95 CDMA system. The proposed design method of the viterbi decoder will be a new method to obtain a required viterbi decoder in a very short time only by supplying the design parameters.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.8 no.1
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• pp.170-178
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• 2004

In this work a high speed 8-error correcting Reed-Solomon decoder is designed using the modified Euclid algorithm. Decoding algorithm of Reed-Solomon codes consists of four steps, those are, compute syndromes, find error-location polynomials, decide error-locations, and determine error values. The decoding speed is increased and the latency is reduced by using the parallel architecture in the syndrome generator and a faster clock speed in the modified Euclid algorithm block. In addition. the error locator polynomial in Chien search block is separated into even and odd terms to increase the overall speed of the decoder. All the functionalities of the decoder are verified first through C++ programs. Verilog is used for hardware description, and then the decoder is synthesized with a $.25{\mu}m$ CMOS TML library. The functionalities of the chip is also verified through test vectors. The clock speed of the chip is 250MHz, and the maximum data rate is 1Gbps.