• Korean Journal of Mathematics
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• 제11권1호
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• pp.57-64
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• 2003

We define $Z_16$ quadratic residue codes in term of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties of quadratic residue codes over a field.

• 대한수학회보
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• 제50권4호
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• pp.1357-1365
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• 2013

We find a lower bound on the number of real/inert imagi-nary/ramified imaginary quadratic extensions of the function field $\mathbb{F}_q(t)$ whose ideal class groups have an element of a fixed order, where $q$ is a power of 2.

• 충청수학회지
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• 제22권4호
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• pp.799-814
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• 2009

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of some class invariants from the generalized Weber functions $\mathfrak{g}_0,\mathfrak{g}_1,\mathfrak{g}_2$ and $\mathfrak{g}_3$ over quadratic number fields with discriminant $D{\equiv}1$ (mod 12).

• 충청수학회지
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• 제26권1호
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• pp.213-219
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• 2013

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, we compute the Galois actions of a class invariant from a generalized Weber function $g_1$ over imaginary quadratic number fields with discriminant $D{\equiv}64(mod72)$.

• 충청수학회지
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• 제24권4호
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• pp.921-925
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• 2011

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}21$ (mod 36).

• 대한수학회보
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• 제58권5호
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• pp.1149-1161
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• 2021

In this paper, we present new bounds on the fundamental units of real quadratic fields ${\mathbb{Q}}({\sqrt{d}})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.

• 충청수학회지
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• 제23권4호
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• pp.853-860
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• 2010

A class invariant is the value of a modular function that generates a ring class field of an imaginary quadratic number field such as the singular moduli of level 1. In this paper, using Shimura Reciprocity Law, we compute the Galois actions of a class invariant from a generalized Weber function $g_2$ over quadratic number fields with discriminant $D{\equiv}-3$ (mod 36).

• Korean Journal of Mathematics
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• 제24권3호
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• pp.567-572
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• 2016

Quadratic residue codes are cyclic codes of prime length n defined over a finite field ${\mathbb{F}}_{p^e}$, where $p^e$ is a quadratic residue mod n. They comprise a very important family of codes. In this article we introduce the generalization of quadratic residue codes defined over Galois rings using the Galois theory.

• 충청수학회지
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• 제27권4호
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• pp.553-562
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• 2014

In this paper we study of densities of the 4-rank of narrow ideal class groups of real quadratic function fields over the rational function field $\mathbb{F}_q(T)$ when $q{\equiv}3$ mod 4.

• 정보보호학회논문지
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• 제1권1호
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• pp.91-96
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• 1991

리듀스드 이원이차형을 사용한 키 교환법이 소개되었다. 이는 실이차체의 클래스군 위에서의 이산대수문제의 어려움을 이용한 것이다.