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鄭春景 관동대학교 1996 關大論文集 Vol.24 No.1
An important concept in dealing with combined binary sequence is the linear complexity of a binary sequence. The linear complexity of a binary sequence is 'the smallest' linear shift register which can be used to generate this sequence. If (s₁) has linear complexty n, then knowledge of 2n consecutive terms of (s₁) completely determine this sequence. Thus no matter how we actually generate (s₁), we must ensure that it has a large linear complexity.
鄭春景 관동대학교 1985 關大論文集 Vol.13 No.3
An element of order 2 in a group is called an involution. By a theorem of Feit-Thompson any finite nonabelian simple group is of even order. And any finite group of even order has an involution. Hence the centralizer of an involusion is always a subgroup of a finite simple group. In general, an important insight into the structure of a finite group can be obtained by studying its involutions and their centralizers. The symmetric group ∑5 of degree has exactly two conjugacy classes of involutions and the centralizer of involution is either the dihedral group order 8 or isomorphic to the direct product C₂×∑₃, where C₂is a cyclic group of order 2 and ∑₃is the symmetric group of degree 3. In this paper we will characterize the symmetric group ∑5 of degree 5 in terms of its involutions and their centralizers. Our main theorem is as follows. THEOREM Let G be a finite group which has exactly two conjugacy classes of involutions. and let u₁and u₂be representatives of these classes. Assume that the following conditions. hold. (ⅰ) CG(u₁) is the dihedral group of order 8, and (ⅱ) CG(u₂) =〈u₂〉×∑₃where ∑₃is the symmetric group of degree 3. Then G is isomorphic to the symmetric group ∑5 of degree 5.
鄭春景 관동대학교 1990 關大論文集 Vol.18 No.1
We can define an addition on the set of all points on a unit circle x²+y²=1 overa field F that gives it an Abelian group structure. Similarly, we can define an addition on the set of all points on an elliptic curve ?? over a field F plus an ideal point O=(∽, ∝) that gives it an Abelian group structure. In this paper, we will study basic properties of these Abelian groups and discuss integer factoring methods by using a unit circle and elliptic curves.