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理学院2021年学术讲座(十)

发布于:2021-05-17 浏览:

报告题目:Characterization of p-ary functions in terms of association schemes

主讲人: 吴严生 教授

主讲人简介:吴严生,博士毕业于南京航空航天大学,目前为南京邮电大学教授。欧洲数学会《数学文摘》、美国数学会《数学评论》评论员。主要研究方向为代数编码理论、密码函数,在环论、密码函数、纠错编码及其在组合数学中的应用等方面做出了一系列优秀成果。近几年以第一作者或通讯作者在IEEE Transactions on Information Theory、IEEE Communications Letters、Designs Codes and Cryptography、Finite Fields and Their Applications、Discrete Applied Mathematics、Discrete Mathematics 等国际知名期刊上发表SCI论文 18 篇。

时间:2021年520日(周四)1030

地点:理学院会议室306

摘要:In this talk, we will obtain an explicit criterion for $p$-ary functions to produce association schemes in terms of their Walsh spectrum. Employing this characterization, we explicitly find a correlation between $p$-ary bent functions and association schemes; to be more exact, we prove that a $p$-ary bent function induces a $p$-class association scheme if and only if the function is weakly regular. As applications of our main criterion, we construct many infinite families of few-class association schemes arising from $p$-ary functions. Furthermore, we present four classes of $p$-ary two-weight linear codes, which are constructed from the association schemes.

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