• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1237-1252
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• 2023

A fundamental problem in coding theory is to find n_q(k, d), the minimum length n for which an [n, k, d]_q code exists. We show that some q-divisible optimal linear codes of dimension 4 over 𝔽_q, which are not of Belov type, can be constructed geometrically using hyperbolic quadrics in PG(3, q). We also construct some new linear codes over 𝔽_q with q = 7, 8, which determine n₇(4, d) for 31 values of d and n₈(4, d) for 40 values of d.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.40 no.3
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• pp.491-496
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• 2015

In this paper, we introduce two classes of optimal codes, [$2^k-1$, k, $2^{k-1}$] simplex codes and [$2^k-1+k$, k, $2^{k-1}+1$] codes, attaining Griesmer bound with equality. We further present and compare the locality of them. The [$2^k-1+k$, k, $2^{k-1}+1$] codes have good locality property as well as optimal code length with given code dimension and minimum distance. Therefore, we expect that [$2^k-1+k$, k, $2^{k-1}+1$] codes can be applied to various distributed storage systems.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.9C
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• pp.537-545
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• 2011

This paper analyzed performance of three dimensional turbo code and turbo ${\Phi}$ codes proposed in the next generation DVB-RCS systems. In the view of turbo ${\Phi}$ codes, we proposed the optimal permutation and puncturing patterns for triple binary input data. We also proposed optimal post-encoder types and interleaving algorithm for three dimensional turbo codes. Based on optimal parameters, we simulated both turbo codes, and we confirmed that the performance of turbo ${\Phi}$ codes are better than that of three dimensional turbo codes. However, the complexity of turbo ${\Phi}$ is more complex than that of three dimensional turbo codes by 18%.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.91-98
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• 2010

One of the most interesting classes of algebraic codes is the class of quadratic residue (QR) codes over a finite field. A natural construction doubling the lengths of QR codes seems to be the double circulant constructions based on quadratic residues given by Karlin, Pless, Gaborit, et. al. In this paper we define a class of triple circulant linear codes based on quadratic residues. We construct many new optimal codes or codes with the highest known parameters using this construction. In particular, we find the first example of a ternary [58, 20, 20] code, which improves the previously known highest minimum distance of any ternary [58, 20] codes.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.921-935
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• 2018

In this study we determine the structure of m-adic residue codes over the non-chain ring $F_q[v]/(v^2-v)$ and present some promising examples of such codes that have optimal parameters with respect to Griesmer Bound. Further, we show that the generators of m-adic residue codes serve as a natural and suitable application for generating reversible DNA codes via a special automorphism and sets over $F_{4^{2k}}[v]/(v^2-v)$.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1327-1337
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• 2022

Zero-difference balanced (ZDB) functions can be applied to many areas like optimal constant composition codes, optimal frequency hopping sequences etc. Moreover, it has been shown that the image set of some ZDB functions is a regular partial difference set, and hence provides strongly regular graphs. Besides, perfect nonlinear functions are zero-difference balanced functions. However, the converse is not true in general. In this paper, we use the decomposition of cyclotomic polynomials into irreducible factors over 𝔽_p, where p is an odd prime to generalize some recent results on ZDB functions. Also we extend a result introduced by Claude et al. [3] regarding zero-difference-p-balanced functions over 𝔽_pⁿ. Eventually, we use these results to construct some optimal constant composition codes.

• The Journal of the Korea institute of electronic communication sciences
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• v.10 no.11
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• pp.1239-1244
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• 2015

In this paper, a new method for finding optimal and short span in Convolutional Self-Doubly Orthogonal(CDO) codes are proposed. This new algorithm based on Parallel Implicitly-Exhaustive search, where we applied dynamic search space reduction methods in order to reduce computational time for finding Optimal Span for R=1/2 rate CDO codes. The simulation results shows that speedup and error correction performance of the new algorithm is better.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.11
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• pp.2397-2404
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• 2012

Underwater acoustic communication has multipath error because of reflection by sea-level and sea-bottom. The multipath of underwater channel causes signal distortion and error floor. In order to improve the performance, it is necessary to employ an iterative coding scheme. Among the iterative coding scheme, turbo codes and LDPC codes are dominant channel coding schemes in recent. This paper concluded that turbo coding scheme is optimal for underwater communications system in aspect to performance, coded word length, and equalizer combining. Also, decision directed phase recovery was used for correcting phase offset induced by multipath. Based on these algorithms, we confirmed the performance in the environment of oceanic experimentation.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.195-203
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• 1998

In [3], we showed that overintegration may be needed to obtain the optimal $H^1$ error rate for the $p$ version. In this paper, we examine the convergence of the $p$ version in practice, and comment on the implementation of the $p$ version in commercial codes. Also, we give an example of a problem with extremely rough coefficients, for which overintegration is necessary to obtain the optimal $H^1$ convergence rate.

• Proceedings of the IEEK Conference
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• 2000.11a
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• pp.157-160
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• 2000

In order to design a low complexity and high performance SOVA decoder for Turbo Codes, we need to analyze the decoding performance with respect to several important design parameters and find out optimal values for them. Thus, we use a scaling factor of soft output and a update depth as the parameters and analyze their effect on the BER performance of the SOVA decoder. finally, we shows the optimal values of them for maximum decoding performance of SOVA decoder for 3GPP complied Turbo codes.