Algebraic Coding Theory and the related studies of algebraic, geometric and analytic natures

点击翻译按钮获取中文摘要

Ozeki, the research project organizer, and the other researchers have developped the methods to study some basic problems in the theory of error-correcting code such as the determination of the covering radii of codes, the existence question of extremal self-dual 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 co-workers attained many remarkable results. More concretely, he has succeeded in the followings :(i) giving the results on extremal singly even self-dual 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 self-dual 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 self-dual 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 self-dual binary [56, 28, 12] codes, and this result has been published by IEEE transaction on Information Theory,The co-researcher F.Uchida has studied the differentiable action of the non-compact Lie group Sp (p, q) on the 4p + 4q - 1 dimensional sphere. The co-researcher N.Murabayashi has studied concerning the zeta functions of the abelian surfaces of CM type, and he has obtained some results on them. The co-researcher 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 co-researcher K.Ueno studies the problem of the boundaries at infinity of the harmonic maps between the Carnot spaces. The co-researcher M.Harada studies self-dual 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