• Journal of Communications and Networks
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• v.15 no.2
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• pp.217-221
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• 2013

Quantum low-density parity-check (LDPC) codes based on the Calderbank-Shor-Steane construction have low encoding and decoding complexity. The sum-product algorithm(SPA) can be used to decode quantum LDPC codes; however, the decoding performance may be significantly decreased by the many four-cycles required by this type of quantum codes. All four-cycles can be eliminated using the entanglement-assisted formalism with maximally entangled states (ebits). The proposed entanglement-assisted quantum error-correcting code based on Euclidean geometry outperform differently structured quantum codes. However, the large number of ebits required to construct the entanglement-assisted formalism is a substantial obstacle to practical application. In this paper, we propose a novel class of entanglement-assisted quantum LDPC codes constructed using classical Euclidean geometry LDPC codes. Notably, the new codes require one copy of the ebit. Furthermore, we propose a construction scheme for a corresponding zigzag matrix and show that the algebraic structure of the codes could easily be expanded. A large class of quantum codes with various code lengths and code rates can be constructed. Our methods significantly improve the possibility of practical implementation of quantum error-correcting codes. Simulation results show that the entanglement-assisted quantum LDPC codes described in this study perform very well over a depolarizing channel with iterative decoding based on the SPA and that these codes outperform other quantum codes based on Euclidean geometries.

• Journal of information and communication convergence engineering
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• v.21 no.4
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• pp.300-305
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• 2023

Audience reactions in response to remote virtual performances must be compressed before being transmitted to the server. The server, which aggregates these data for group insights, requires a distribution code for the transfer. Recently, distributed learning algorithms such as federated learning have gained attention as alternatives that satisfy both the information security and efficiency requirements. In distributed learning, no individual user has access to complete information, and the objective is to achieve a learning effect similar to that achieved with the entire information. It is therefore important to distribute interdependent information among users and subsequently aggregate this information following training. In this paper, we present a new extension technique for minimal code that allows a new minimal code with a different length and Hamming weight to be generated through the product of any vector and a given minimal code. Thus, the proposed technique can generate minimal codes with previously unknown parameters. We also present a scenario wherein these combined methods can be applied.

• ETRI Journal
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• v.31 no.5
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• pp.585-592
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• 2009

This paper presents a method for decoding high minimal distance ($d_{min}$) short codes, termed Cortex codes. These codes are systematic block codes of rate 1/2 and can have higher$d_{min}$ than turbo codes. Despite this characteristic, these codes have been impossible to decode with good performance because, to reach high $d_{min}$, several encoding stages are connected through interleavers. This generates a large number of hidden variables and increases the complexity of the scheduling and initialization. However, the structure of the encoder is well suited for analog decoding. A proof-of-concept Cortex decoder for the (8, 4, 4) Hamming code is implemented in subthreshold 0.25-${\mu}m$ CMOS. It outperforms an equivalent LDPC-like decoder by 1 dB at BER=$10^{-5}$ and is 44 percent smaller and consumes 28 percent less energy per decoded bit.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.359-368
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• 2018

In this paper, we investigate quasi-cyclic codes over the ring $R={\mathbb{F}}_2+v{\mathbb{F}}_2$, where $v^2=v$. We investigate the structure of generators for one-generator quasi-cyclic codes over R and their minimal spanning sets. Moreover, we find the rank and a lower bound on minimum distances of free quasi-cyclic codes over R. Further, we find a relationship between cyclic codes over a different ring and quasi-cyclic codes of index 2 over R.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.169-179
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• 2009

Let P be a (n, n − 1, j)-poset, which is a partially ordered set of cardinality n with n − 1 maximal elements and $j(1{\leq}j{\leq}n-1)$ minimal elements, and $P^*$ the dual poset of P. In this paper, we obtain two types of incidence codes of nonempty proper subset S of P and $P^*$, respectively, by using Bogart's method [1] (see Theorem 3.3).

• 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 Korean Mathematical Society
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• v.58 no.3
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• pp.571-595
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• 2021

In this paper we study the algebraic structure of ℤ_pℤ_p[u]/k>-cyclic codes, where u^k = 0 and p is a prime. A ℤ_pℤ_p[u]/k>-linear code of length (r + s) is an R_k-submodule of ℤ^r_p × R^s_k with respect to a suitable scalar multiplication, where R_k = ℤ_p[u]/k>. Such a code can also be viewed as an R_k-submodule of ℤ_p[x]/r - 1> × R_k[x]/s - 1>. A new Gray map has been defined on ℤ_p[u]/k>. We have considered two cases for studying the algebraic structure of ℤ_pℤ_p[u]/k>-cyclic codes, and determined the generator polynomials and minimal spanning sets of these codes in both the cases. In the first case, we have considered (r, p) = 1 and (s, p) ≠ 1, and in the second case we consider (r, p) = 1 and (s, p) = 1. We have established the MacWilliams identity for complete weight enumerators of ℤ_pℤ_p[u]/k>-linear codes. Examples have been given to construct ℤ_pℤ_p[u]/k>-cyclic codes, through which we get codes over ℤ_p using the Gray map. Some optimal p-ary codes have been obtained in this way. An example has also been given to illustrate the use of MacWilliams identity.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.773-793
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• 2001

The explicit expressions for the 2n+1 primitive idempotents in R/sub pⁿ/ = F[x]/< x/sup pⁿ/ -1>, where F is the field of prime power order q and the multiplicative order of q modulo pⁿ is ø(pⁿ)/2(n≥1 and p is an odd prime), are obtained. An algorithm for computing the generating polynomials of the minimal QR cyclic codes of length pⁿ, generated by these primitive idempotents, is given and hence some bounds on the minimum distance of some QR codes of prime length over GF(q)(q=2, 3, ...) are obtained.

• Nuclear Engineering and Technology
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• v.52 no.5
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• pp.1002-1007
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• 2020

The purpose of the current study was to evaluate a spectrum formulation set employed to modify the neutron spectrum of D-D fusion neutrons in a IS plasma focus device using GEANT4, MCNPX2.6, and FLUKA codes. The set consists of a moderator, reflector, collimator and filters of fast neutron and gamma radiation, which placed on the path of 2.45 MeV neutron energy. The treated neutrons eliminate cancerous tissue with minimal damage to other healthy tissue in a method called neutron therapy. The system optimized for a total neutron yield of 10⁹ (n/s). The numerical results indicate that the GEANT4 code for the cubic geometry in the Beam Shaping Assembly 3 (BSA3) is the best choice for the energy of epithermal neutrons.

• Nuclear Engineering and Technology
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• v.48 no.2
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• pp.419-433
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• 2016

One of the important severe accident management measures in the Light Water Reactors is water injection to the reactor core. The related phenomena are investigated by performing experiments and computer simulations. One of the most widely known is the QUENCH test-program. A number of analyses on QUENCH tests have also been performed by different computer codes for code validation and improvements. Unfortunately, any deterministic computer simulation is not free from the uncertainties. To receive the realistic calculation results, the best estimate computer codes should be used for the calculation with combination of uncertainty and sensitivity analysis of calculation results. In this article, the QUENCH-03 and QUENCH-06 experiments are modelled using ASTEC and RELAP/SCDAPSIM codes. For the uncertainty and sensitivity analysis, SUSA3.5 and SUNSET tools were used. The article demonstrates that applying the best estimate approach, it is possible to develop basic QUENCH input deck and to develop the two sets of input parameters, covering maximal and minimal ranges of uncertainties. These allow simulating different (but with the same nature) tests, receiving calculation results with the evaluated range of uncertainties.