• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.69-86
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• 2017

The point $P{\in}{\mathbb{P}}^2$ is referred to as a Galois point for a nonsingular plane algebraic curve C if the projection ${\pi}_P:C{\rightarrow}{\mathbb{P}}^1$ from P is a Galois covering. In contrast, the point $P^{\prime}{\in}C^{\prime}$ is referred to as a weak Galois Weierstrass point of a nonsingular algebraic curve C' if P' is a Weierstrass point of C' and a total ramification point of some Galois covering $f:C^{\prime}{\rightarrow}{\mathbb{P}}^1$. In this paper, we discuss the following phenomena. For a nonsingular plane curve C with a Galois point P and a double covering ${\varphi}:C{\rightarrow}C^{\prime}$, if there exists a common ramification point of ${\pi}_P$ and ${\varphi}$, then there exists a weak Galois Weierstrass point $P^{\prime}{\in}C^{\prime}$ with its Weierstrass semigroup such that H(P') = or , which is a semigroup generated by two positive integers r and 2r + 1 or 2r - 1, such that P' is a branch point of ${\varphi}$. Conversely, for a weak Galois Weierstrass point $P^{\prime}{\in}C^{\prime}$ with H(P') = or , there exists a nonsingular plane curve C with a Galois point P and a double covering ${\varphi}:C{\rightarrow}C^{\prime}$ such that P' is a branch point of ${\varphi}$.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.263-286
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• 2016

We discuss relations between Galois coverings of compact Riemann surfaces and their Jacobi varieties. We prove a theorem of a kind of Galois correspondence for Abelian subvarieties of Jacobi varieties. We also prove a theorem on the sets of points in Jacobi varieties fixed by Galois group actions.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.11 no.1
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• pp.53-63
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• 1986

In this paper the decoder of nonbinary code satisfying R>1/t has been designed and constructed, where R is the code rate and t is the error correcting capability. In order to design the error trapping decoder, the concept of covering monomial is used and them the decoder system using the (15, 11) Reed-Solomon code is implemented. Without Galois Fiedl multiplication and division circuits, the decoder system is simply constructed. In the decoding process, it takes 60clocks to decode one code word. Two symbol errors and eight binary burst errors are simultaneously corrected. This coding system is shown to be efficient when the channel error probability is approximately from $5{\times}10^-4$~$5{\times}10^-5$.