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

Ozeki等人发展了研究纠错码理论中一些基本问题的方法，如码的覆盖半径的确定、极值自对偶码的存在性问题、码的陪集重量分布、码的影子理论、码类的质量公式、码的分类问题等。他和同事们取得了许多显著的成果。更具体地说，他在以下方面取得了成功：（i）给出了极值单偶自对偶二元[40，20，8]码的结果，其中包括覆盖半径为7的码，这些结果已在《离散数学》上发表;（ii）发展了一种处理覆盖半径问题和确定双偶自对偶二元码的完全陪集重量分布的决定性方法，并利用这种方法确定了双偶自对偶二元码的完全陪集重量分布和完全陪集重量分布 ...更多信息 d是极值双偶自对偶二元[40，20，8]码的覆盖半径，这一结果已在Theoretical Computer Science上发表. Vol.235，（iii）在很大程度上锐化了（ii）中的方法，并且他确定了极值双偶自对偶二元码的覆盖半径[56，28，12]，并且该结果已由IEEE transaction on Information Theory发表。q）在4p +4 q- 1维球面上。N.Murabayashi等人对CM型交换曲面的zeta函数进行了研究，得到了一些结果。共同研究员T.佐野研究了Kac代数的构造，以及标准型自同构的交换性问题，他正在准备研究论文。K.Ueno研究了卡诺空间之间调和映射在无穷远处的边界问题。Harada研究了有限环上的自对偶码及其与其它离散数学子领域的关系，特别是幺模格与组合设计的关系。少

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