Project/Area Number  09440003 
Research Category 
GrantinAid for Scientific Research (B).

Section  一般 
Research Field 
Algebra

Research Institution  Faculty of Science, Yamagata University 
Principal Investigator 
OZEKI Michio Department of Mathematical Sciences, Professor, 理学部, 教授 (90087073)

CoInvestigator(Kenkyūbuntansha) 
UENO Keisuke Department of Mathematical Sciences, Research Associate, 理学部, 助手 (10250911)
HARADA Masaaki Department of Mathematical Sciences, Research Associate, 理学部, 助手 (90292408)
渡辺 伸一 山形大学, 理学部, 講師 (40007175)
内田 吉昭 山形大学, 理学部, 助教授 (80280890)
平吹 慎吉 山形大学, 理学部, 助教授 (70007136)
SANO Takashi Department of Mathematical Sciences, Associate Professor, 理学部, 助教授 (20250912)
MURABAYASHI Naoki Department of Mathematical Sciences, Associate Professor, 理学部, 助教授 (80261676)
澤田 秀樹 山形大学, 理学部, 助教授 (30095856)
井伊 清隆 山形大学, 理学部, 助教授 (10007180)
鹿野 健 山形大学, 教育学部, 教授 (90020669)
平松 豊一 法政大学, 工学部, 教授 (40029674)
尾方 隆司 山形大学, 理学部, 教授 (10042425)
大池 宏清 山形大学, 理学部, 教授 (20007165)
UCHIDA Fuichi Department of Mathematical Sciences, Professor, 理学部, 教授 (90028126)

Project Fiscal Year 
1997 – 2000

Project Status 
Completed(Fiscal Year 2000)

Budget Amount *help 
¥11,300,000 (Direct Cost : ¥11,300,000)
Fiscal Year 2000 : ¥2,500,000 (Direct Cost : ¥2,500,000)
Fiscal Year 1999 : ¥2,500,000 (Direct Cost : ¥2,500,000)
Fiscal Year 1998 : ¥2,600,000 (Direct Cost : ¥2,600,000)
Fiscal Year 1997 : ¥3,700,000 (Direct Cost : ¥3,700,000)

Keywords  binary codes / ternary codes / the covering radius / coset weight distributions / Jacobi polynomials of codes / 2元符号 / 3元符号 / 被覆半径 / コセット重み分布 / ヤコビ多項式 / 不変式環 
Research Abstract 
Ozeki, the research project organizer, and the other researchers have developped the methods to study some basic problems in the theory of errorcorrecting code such as the determination of the covering radii of codes, the existence question of extremal selfdual codes, the coset weight distributions of codes, the shadow theory of codes, the mass formulas for the classes of codes, the classification problem of codes. And he and the coworkers attained many remarkable results. More concretely, he has succeeded in the followings : (i) giving the results on extremal singly even selfdual binary [40, 20, 8] codes, among which a code with the covering radius of 7 is included, and this results have been published by Discrete Mathematics, (ii) developing a decisive method to treat the covering radius problem and the determination of the complete coset weight distributions of doubly even selfdual binary codes, and by using this method he has determined the complete coset weight distributions an
… More
d the covering radius of extremal doubly even selfdual binary [40, 20, 8] codes, this results has been published by Theoretical Computer Science. Vol. 235, (iii) sharpening the method in (ii) to the large extent and he has determined the covering radius of extremal doubly even selfdual binary [56, 28, 12] codes, and this result has been published by IEEE transaction on Information Theory, The coresearcher F.Uchida has studied the differentiable action of the noncompact Lie group Sp (p, q) on the 4p + 4q  1 dimensional sphere. The coresearcher N.Murabayashi has studied concerning the zeta functions of the abelian surfaces of CM type, and he has obtained some results on them. The coresearcher T.Sano has studied the construction of the Kac algebras, and the commutavity problem of the automorphisms of the standard type, and he is preparing the research papers. The coresearcher K.Ueno studies the problem of the boundaries at infinity of the harmonic maps between the Carnot spaces. The coresearcher M.Harada studies selfdual codes over finite rings, and the relations of the codes with other subareas of disctrete mathematics, espacially the relations between the unimodular lattices and the combinatorial designs. Less
