A study of the interacting area among the theory of quadratic forms and the theory of modular forms and the algebraic coding theory

本研究是在2002年至2004年期间在教育、文化、体育、科学和技术部资助的补助金下进行的。在申请中，主要研究者提出了五个研究目的：(1)研究编码理论与模形式理论之间的相互作用，(2)研究二元自对偶码和三级自对偶码构成的格，(3)n维格的覆盖半径问题，(4)非自对偶线性码的覆盖半径问题，(5)编码理论与密码学之间的相互作用。至于目的(1)，我们取得了一些成果，并进行了4次演讲，正在准备研究论文。关于(2)，我们已经发表了一篇研究论文，正在准备一篇。至于(3)结果不成熟，不适合写论文。关于(4)，我们做了两次报告，正在准备一些研究论文。没有实现这一目的的实际活动(5)。除了研究目的外，我们还发表了三篇研究论文。

The present research has been done in the period between year 2002 and 2004 under the GRANT-IN-AID sponcered by the Ministry of Education, Culture, Sports, Science and Technology.In the application the head investigator raised five reseach purposes : (1)a study of the ineraction between the coding theory and the theory of modular forms, (2)a study of the lattices constructed from the binary self-dual code and the tertiary self dual codes, (3)the covering radius problem for the n-dimensional lattices, (4)the covering radius problem for non self-dual linear codes, (5)an interaction bewtween the coding theory and the cryptology.As to the purpose (1) we get some results and gave 4 talks and are preparing the research papers.As to (2) we have published one research paper and are preparing one paper.As to (3) the result is not mature for writing a paper.As to (4) we gave two talks and are preparing some research papers.There is no actual activity fot the purpose (5).Besides the research purpose we have published three research papers.