报告题目：On $ Z_{p} Z_{p^k}$-additive codes and their duality

报告人：施敏加  安徽大学002cc白菜资讯

报告时间：2019年5月22日 16:00-17:00

报告地点：002cc白菜资讯三楼报告厅

报告摘要：In this paper, two different Gray like maps from $Z{_p}^\alpha\times Z_{p^k}^\beta$ to $Z{_p}^n$, $n={\alpha+\beta p^{k-1}}$, denoted by $\phi$ and $\varphi$, respectively, are presented, where $p$ is a prime number. We have determined the connection between the weight enumerators among the image codes under these two mappings.  We show that if $C$ is a $Z{_p} Z_{p^k}$-additive code, and $C^\bot$ is its dual, then the weight enumerators of the image $p$-ary codes $\phi(C)$ and $\varphi(C^\bot)$ are formally dual. This is a partial generalization of [D. S. Krotov, On $Z_{2^k}$-dual binary codes, IEEE Transactions on Information Theory, 2007, 53(4): 1532--1537], and the result is generalized to odd characteristic $p$ and mixed alphabet $Z{_p} Z_{p^2}\ldots Z_{p^k}$. Additionally, a construction of $1$-perfect additive codes in the mixed $Z{_p} Z_{p^2}\ldots Z_{p^k}$ alphabet % with distance $d^\diamond$ is given.

报告人简介：施敏加，教授，博士研究生导师，安徽省学术与技术带头人后备人选，曾获安徽省自然科学一等奖和第二届“安徽省青年数学奖”。主持了国家自然科学基金3项，安徽省自然科学基金杰出青年基金等省部级重点项目7项。 以第一作者在Elsevier出版社出版英文专著1本， 在 《IEEE Transaction on Information Theory》、《Designs, Codes and Cryptography》、《Finite Fields and Their Applications》等国内外重要学术期刊上发表学术论文80余篇，其中 SCI收录50余篇。曾应邀访问法国高等电信专科学校2个月，新加坡南洋理工大学1年，2014年以来多次应邀访问南开大学陈省身数学研究所。