• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1175-1186
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• 2014

We construct new binary optimal self-dual codes of length 50. We develop a construction method for binary self-dual codes with a fixed-point-free automorphism of order 2. Using this method, we find new binary optimal self-dual codes of length 52. From these codes, we obtain Lee-optimal self-dual codes over the ring $\mathbb{F}_2+u\mathbb{F}_2$ of lengths 25 and 26.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.211-219
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• 2022

We study MDS(maximum distance separable) self-dual codes over Galois ring R = GR(2^m, r). We prove that there exists an MDS self-dual code over R of length n if (n - 1) divides (2^r - 1), and 2^m divides n. We also provide the current state of the problem for the existence of MDS self-dual codes over Galois rings.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.255-270
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• 2020

We studied the MDS self-dual codes over finite chain rings. We stated the projection and lifting of codes over the finite chain rings with respect to the MDS self-dual codes, and then we applied the results to the MDS self-dual codes over Galois rings.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.653-664
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• 2012

We study the abstract structure of the automorphism group of the ternary self-dual code of length 8 and give its convenient presentation by generators.

• Journal of Positioning, Navigation, and Timing
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• v.7 no.1
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• pp.1-14
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• 2018

The Global Positioning System (GPS) provides more accurate positioning estimation performance by processing L1 and L2 signals simultaneously through dual frequency signal processing technology at the L-band rather than using only L1 signal. However, if anti-spoofing (AS) mode is run at the GPS, the precision (P) code in L2 signal is encrypted to Y code (or P(Y) code). Thus, dual frequency signal processing can be done only when the effect of P(Y) code is eliminated through the L2 signal processing technology. To do this, a codeless technique or semi-codeless technique that can acquire phase measurement information of L2 signal without information about W code should be employed. In this regard, this paper implements L2 signal processing technology where two typical codeless techniques and four typical semi-codeless techniques of previous studies are applied and compares their performances to discuss the optimal technique selection according to implementation environments and constraints.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.3
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• pp.181-194
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• 2023

Let GR(2^m, r) be a Galois ring with even characteristic. We are interested in the existence of MDS(Maximum Distance Separable) self-dual codes over GR(2^m, r). In this paper, we prove that there exists an MDS self-dual code over GR(2^m, r) with parameters [n, n/2, n/2 + 1] if (n - 1) | (2^r - 1) and 8 | n.

• Journal of Positioning, Navigation, and Timing
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• v.4 no.4
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• pp.151-160
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• 2015

GPS L2C signal is a recently added civil signal to L2 frequency and is constructed by time division multiplexing of civil moderate (L2-CM) and civil long (L2-CL) code signals. While the L2-CM code is 20 ms-periodic and modulates satellite navigation message, the L2-CL code is 1.5s-periodic with 767,250 chips long code sequence and carries no data. Therefore, the L2-CL code signal allows receivers to perform a very long coherent integration. However, due to the length of the L2-CL code, the acquisition of the L2-CL code signal may take too long or require too much hardware resources. In this paper, we propose a three-step ultra-fast L2-CL code acquisition (TSCLA) technique for dual band GPS receivers. In the proposed TSCLA technique, a dual band GPS receiver sequentially acquires the coarse/acquisition (C/A) code signal at L1 frequency, the L2-CM code signal, and the L2-CL code signal to minimize mean acquisition time (MAT). The theoretical performance analysis and numerous Monte Carlo simulations show the significant advantage of the proposed TSCLA technique over conventional techniques introduced in the literature.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.487-493
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• 2009

We study the group structure of the automorphism group of the ternary self-dual tetracode of length 4.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.1
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• pp.127-132
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• 2013

In this paper, we design the physical layer of Guardian modem for wireless public networks. The physical layer is composed of a dual-band RF (Radio Frequency) transceiver and a baseband-processor with quasi-orthogonal codes. The 2.4/5GHz dual-band RF transceiver can overcome the communication difficulty of dense 2.4GHz band for wireless public environment. Also the quasi-orthogonal code can reduce the required ASIC (Application Specific Integrated Circuit) design area. Finally, we analyze the performance of the developed system in viewpoint of data rate, BER (Bit Error Rate), PER (Packet Error Rate). Moreover we verify the performance of the dual-band RF communication.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.829-844
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• 2023

In this paper, we present a new construction for self-dual codes that uses the concept of double bordered construction, group rings, and reverse circulant matrices. Using groups of orders 2, 3, 4, and 5, and by applying the construction over the binary field and the ring F₂ + uF₂, we obtain extremal binary self-dual codes of various lengths: 12, 16, 20, 24, 32, 40, and 48. In particular, we show the significance of this new construction by constructing the unique Extended Binary Golay Code [24, 12, 8] and the unique Extended Quadratic Residue [48, 24, 12] Type II linear block code. Moreover, we strengthen the existing relationship between units and non-units with the self-dual codes presented in [10] by limiting the conditions given in the corollary. Additionally, we establish a relationship between idempotent and self-dual codes, which is done for the first time in the literature.