• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.443-460
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• 2023

A binary linear code is said to be a ℤ₂-double cyclic code if its coordinates can be partitioned into two subsets such that any simultaneous cyclic shift of the coordinates of the subsets leaves the code invariant. These codes were introduced in [6]. A ℤ₂-double cyclic code is called reversible if reversing the order of the coordinates of the two subsets leaves the code invariant. In this note, we give necessary and sufficient conditions for a ℤ₂-double cyclic code to be reversible. We also give a relation between reversible ℤ₂-double cyclic code and LCD ℤ₂-double cyclic code for the separable case and we present a few examples to show that such a relation doesn't hold in the non-separable case. Furthermore, we list examples of reversible ℤ₂-double cyclic codes of length ≤ 10.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.2
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• pp.1-10
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• 1997

In this paper, an improved lower bound on the burst-error correcting capability of th ecyclic product code is presented and through the analysis of this new bound clustered cyclic product (CCP abbr.)code is proposed. The CCP code, to improve the burst-error correcting capability, combines the idea of clustering and the transmission method of cyclic product code. That is, a cluster which is defined in this paper as a group of consecutive code symbols is employed as a new transmission unit to the code array transmission of cyclic product code. the burst-error correcting capability of the CCP code is improved without a loss in the random-error correcting capability and performance comparison in the digital video camera records (DVCR) system shows the superiority of the proposed CCP code over conventional product codes.

• East Asian mathematical journal
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• v.17 no.1
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• pp.167-174
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• 2001

We find the generalized Hamming weights of cyclic linear q-ary codes which are generated by a codeword of weight 2, and of any length.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.12
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• pp.1700-1706
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• 2016

To improve the number of simultaneous transmissions of machine-to-machine traffic in a spread spectrum ALOHA channel, we propose a new spreading technique called doubly truncated cyclic code shift keying (DTCCSK). By truncating the codeset of cyclic code shift keying, DTCCSK freely adjusts the spreading factor and the symbol length. As a result, DTCCSK exhibits both a high spectral efficiency of M-ary signaling and low implementation complexity of a direct sequence.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.419-437
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• 2019

This paper investigates skew ${\Theta}-{\lambda}$-constacyclic codes over $R=F_0{\oplus}F_1{\oplus}{\cdots}{\oplus}F_{k-1}$, where $F{_i}^{\prime}s$ are finite fields. The structures of skew ${\lambda}$-constacyclic codes over finite commutative semi-simple rings and their duals are provided. Moreover, skew ${\lambda}$-constacyclic codes of arbitrary length are studied under a new definition. We also show that a skew cyclic code of arbitrary length over finite commutative semi-simple rings is equivalent to either a cyclic code over R or a quasi-cyclic code over R.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.529-537
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• 2014

The paper introduces a new product of polynomials defined over a field. It is a generalization of the ordinary product with inner polynomial getting non-overlapping segments obtained by multiplying with coefficients and variable with expanding powers. It has been called 'Ordered Power Product' (OPP). Considering two rings of polynomials $R_m[x]=F[x]modulox^m-1$ and $R_n[x]=F[x]modulox^n-1$, over a field F, the paper then considers the newly introduced product of the two polynomial rings. Properties and algebraic structure of the product of two rings of polynomials are studied and it is shown to be a ring. Using the new type of product of polynomials, we define a new product of two cyclic codes and devise a method of getting a cyclic code from the 'ordered power product' of two cyclic codes. Conditions for the OPP of the generators polynomials of component codes, giving a cyclic code are examined. It is shown that OPP cyclic code so obtained is more efficient than the one that can be obtained by Kronecker type of product of the same component codes.

• Journal of the Korean Institute of Telematics and Electronics
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• v.22 no.5
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• pp.24-28
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• 1985

In this paper, the cyclic product codes which are capable of correcting random erros and burst errors simultaneously have been designed and constructed. First, the procedure for product of two cyclic codes is shown and thin the encoder and decoder system using the (7,4) cyclic Hamming code and the (3,1) cyclic code is implemented. The micro-computer is used for experiment and the system consists of encoder, decoder and interface circuits. The encoder of cyclic product code is implemented by interlacing encoders while the decoder is implemented by cascading decoders that interlace error trapping decoders. In conclusion, cyclic product codas are easily decodable and are capable of correcting four random errors and eight-burst errors. Better performance is obtained with low error rate.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.1
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• pp.83-91
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• 1993

In the digital transmission system, cyclic redundancy check(CRC) code is widely used because it is easy to be implemented and has good performance in error detection. CRC code generator consists of several shift registers and modulo 2 adders. After manipulation of input data stream in the encoder, the remaining value of shift registers becomes CRC code. At the receiving side, error can be detected and corrected by CRC codes immediately transmitted after data stream. But, in the high speed system such as an A TM switch, it is difficult to implement the serial CRC encoder because of speed limitation of available semiconductor devices. In this paper, we propose the efficient parallel CRC encoder and syndrome calculator to solve the speed problem in implementing these functions using the existing semiconductor technology.

• Journal of IKEEE
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• v.16 no.1
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• pp.51-55
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• 2012

In this paper, we propose to employ a ternary sequence as a cyclic code shift keying (CCSK) modulation sequence. And we simulate the performance in a frequency hopping spread spectrum/time division multiple access (FHSS/TDMA) system with CCSK. Wireless channel is modeled as Rayleigh fading channel. From the simulation results, it is demonstrated that the system adopting the ternary sequence as a CCSK sequence has higher performance than that with a random sequence.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.6
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• pp.42-48
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• 2010

Joint Tactical Information Distribution System (JTIDS) uses cyclic code shift keying (CCSK) for baseband symbol modulation, in which 5-bit information is mapped to one of thirty two 32-chip sequences. It is a kind of direct sequence based spread spectrum communication. In this paper, the performance of non-coherent detection of CCSK using non-orthogonal 32-chip sequence is evaluated. And a 32-chip sequence with better performance is also proposed and compared with the conventional one.