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한성휴 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.5
In this paper, we prove that for all odd prime powers q there exist MDS(maximum distance separable) self-dual codes over Fq2 for all even lengths up to q + 1. Additionally, we prove that there exist MDS self-dual codes of length four over Fq for all q > 2; q ≠ 5.
On the idempotents of cyclic codes over $\mathbb{F}_{2^t}$
한성휴 강원경기수학회 2022 한국수학논문집 Vol.30 No.4
We study cyclic codes of length $n$ over $\mathbb{F}_{2^t}$. Cyclic codes can be viewed as ideals in $\mathcal{R}_n = \mathbb{F}_{2^t}[x]/(x^n - 1)$. It is known that there is a unique generating idempotent for each ideal. Let $e(x) \in \mathcal{R}_n$. If $t = 1$ or $t = 2$, then there is a necessary and sufficient condition that $e(x)$ is an idempotent. But there is no known similar result for $t \geq 3$. In this paper we give an answer for this problem.
CONSTRUCTION OF SELF-DUAL CODES OVER F2 + uF2
한성휴,이혜숙,이윤진 대한수학회 2012 대한수학회보 Vol.49 No.1
We present two kinds of construction methods for self-dual codes over F2 + uF2. Specially, the second construction (respectively,the rst one) preserves the types of codes, that is, the constructed codes from Type II (respectively, Type IV) is also Type II (respectively, Type IV). Every Type II (respectively, Type IV) code over F2 + uF2 of free rank larger than three (respectively, one) can be obtained via the second construction (respectively, the rst one). Using these constructions, we update the information on self-dual codes over F2+uF2 of length 9 and 10,in terms of the highest minimum (Hamming, Lee, or Euclidean) weight and the number of inequivalent codes with the highest minimum weight.
ON THE EXISTENCE OF MDS SELF-DUAL CODES OVER FINITE CHAIN RINGS
한성휴 충청수학회 2020 충청수학회지 Vol.33 No.2
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.
Self-dual codes and antiorthogonal matrices over Galois rings
한성휴 충청수학회 2018 충청수학회지 Vol.31 No.2
We study self-dual codes over Galois rings using the building-up construction method. In the construction, the existence of an antiorthogonal matrix is very important. In this study, we examine the existence problem of an antiorthogonal matrix over Galois rings.
Two-Dimensional Joint Bayesian Method for Face Verification
한성휴,이일용,안정호 한국정보처리학회 2016 Journal of information processing systems Vol.12 No.3
The Joint Bayesian (JB) method has been used in most state-of-the-art methods for face verification. However, since the publication of the original JB method in 2012, no improved verification method has been proposed. A lot of studies on face verification have been focused on extracting good features to improve the performance in the challenging Labeled Faces in the Wild (LFW) database. In this paper, we propose an improved version of the JB method, called the two-dimensional Joint Bayesian (2D-JB) method. It is very simple but effective in both the training and test phases. We separated two symmetric terms from the three terms of the JB log likelihood ratio function. Using the two terms as a two-dimensional vector, we learned a decision line to classify same and not-same cases. Our experimental results show that the proposed 2D-JB method significantly outperforms the original JB method by more than 1% in the LFW database.
Nonexistence of some extremal self-dual codes
한성휴,이준복 대한수학회 2006 대한수학회지 Vol.43 No.6
It is known that ifC is an [24m + 2 l;12m + l;d] self-dual binary linear code with 0 l < 11, then d 4m + 4. Wepresent a sucient condition for the nonexistence of extremal self-dual binary linear codes with d = 4 m + 4 ;l = 1 ;2;3;5. Fromthe sucient condition, we calculate m's which correspond to thenonexistence of some extremal self-dual binary linear codes. Inparticular, we prove that there are innitely many suchm's. Wealso give similar results for additive self-dual codes overGF(4) oflength n = 6 m + 1.
MDS SELF-DUAL CODES OVER GALOIS RINGS WITH EVEN CHARACTERISTIC
한성휴 충청수학회 2023 충청수학회지 Vol.36 No.3
Let GR(2m, r) be a Galois ring with even characteris-tic. We are interested in the existence of MDS(Maximum DistanceSeparable) self-dual codes over GR(2m, r). In this paper, we provethat there exists an MDS self-dual code over GR(2m, r) with pa-rameters [n, n/2, n/2 + 1] if (n − 1) | (2r − 1) and 8 | n.