• Journal of the Korean Mathematical Society
• /
• v.44 no.5
• /
• pp.1139-1162
• /
• 2007

We examine the main linear coding theory problem and study the structure of optimal linear codes over the ring ${\mathbb{Z}}_m$. We derive bounds on the maximum Hamming weight of these codes. We give bounds on the best linear codes over ${\mathbb{Z}}_8$ and ${\mathbb{Z}}_9$ of lengths up to 6. We determine the minimum distances of optimal linear codes over ${\mathbb{Z}}_4$ for lengths up to 7. Some examples of optimal codes are given.

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

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.6
• /
• pp.1557-1565
• /
• 2022

In this paper, Glift codes, generalized lifted polynomials, matrices are introduced. The advantage of Glift code is "distance preserving" over the ring R. Then optimal codes can be obtained over the rings by using Glift codes and lifted polynomials. Zero divisors are classified to satisfy "distance preserving" for codes over non-chain rings. Moreover, Glift codes apply on MDS codes and MDS codes are obtained over the ring 𝓡 and the non-chain ring 𝓡_e,s.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.2011-2023
• /
• 2015

This paper determines the structures of one-homogeneous weight codes over finite chain rings and studies the algebraic properties of these codes. We present explicit constructions of one-homogeneous weight codes over finite chain rings. By taking advantage of the distance-preserving Gray map defined in [7] from the finite chain ring to its residue field, we obtain a family of optimal one-Hamming weight codes over the residue field. Further, we propose a generalized method that also includes the examples of optimal codes obtained by Shi et al. in [17].

• Proceedings of the IEEK Conference
• /
• 2004.08c
• /
• pp.645-648
• /
• 2004

In this paper, we drive a theoretical performance of complementary code keying (CCK) codes on additive white Gaussian noise (AWGN) channel. The CCK codes can be demodulated by the optimal maximum likelihood decoding method and sub-optimal correlation magnitude decoding algorithm. We calculate the bit error rate (BER) and symbol or codeword error rate (SER) of the CCK codes using the above mentioned two decoding algorithms. To derive the error performance, we use the weigh distributions and cross-correlation distributions of CCK codes.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.31 no.9C
• /
• pp.825-830
• /
• 2006

Capacity-approaching codes using iterative decoding have been the main subject of research activities during past decade. Especially, LDPC codes show the best asymptotic performance and density evolution has been used as a powerful technique to analyze and design good LDPC codes. In this paper, we apply density evolution with a Gaussian approximation to the concatenated zigzag (CZZ) codes by considering both flooding and two-way schedulings. Based on this density evolution analysis, the threshold values are computed for various CZZ codes and the optimal structure of CZZ codes for various code rates are obtained. Also, simulation results are provided to conform the analytical results.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.25 no.6B
• /
• pp.1100-1105
• /
• 2000

The most widely used radar pulse compression technique is correlation processing using Barker code. This technique enhances detection sensitivity but, unfortunately, suffers from the addition of range sidelobes which sometimes will degrade the performance of radar systems. In this paper, our proposed optimal algorithm eliminates the sidelobes at the cost of additional processing and is evaluated in the presence of Doppler shift. We then propose optimal codes with regard to the proposed algorithm and the performance is compared against the traditional correlation processing with Barker codes. The proposed processing using optimal codes will be shown to be superior over the traditional processing in the presence of Doppler shift.

• Journal of the Korean Mathematical Society
• /
• v.59 no.1
• /
• pp.193-204
• /
• 2022

We present construction methods for free self-orthogonal (self-dual or Type II) codes over ℤ₄[v]/〈v² + 2v〉 which is one of the finite commutative local non-chain Frobenius rings of order 16. By considering their Gray images on ℤ₄, we give a construct method for a code over ℤ₄. We have some new and optimal codes over ℤ₄ with respect to the minimum Lee weight or minimum Euclidean weight.

• ETRI Journal
• /
• v.40 no.3
• /
• pp.291-302
• /
• 2018

The deployment of an incremental hybrid decode-amplify and forward relaying scheme is a promising and superior solution for cellular networks to meet ever-growing network traffic demands. However, the selection of a suitable relaying protocol based on the signal-to-noise ratio threshold is important in realizing an improved quality of service. In this paper, an incremental hybrid relaying protocol is proposed using polar codes. The proposed protocol achieves a better performance than existing turbo codes in terms of capacity. Simulation results show that the polar codes through an incremental hybrid decode-amplify-and-forward relay can provide a 38% gain when ${\gamma}_{th(1)}$ and ${\gamma}_{th(2)}$ are optimal. Further, the channel capacity is improved to 17.5 b/s/Hz and 23 b/s/Hz for $2{\times}2$ MIMO and $4{\times}4$ MIMO systems, respectively. Monte Carlo simulations are carried out to achieve the optimal solution.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.41 no.10
• /
• pp.1176-1178
• /
• 2016

We propose some binary locally repairable codes with locality 2 uising a parity-check matrix. The minimum distance of the proposed codes is 6. The proposed codes are optimal in the sense of achieving the upper bound of dimension for given length, minimum distance, and locality.