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 报告人 郑大彬 举办单位 科技处、学科办、研究生处、数统学院 报告题目 Constructions of involutions over finite fields 报告时间 2019年11月5日 11：00-12：00 报告地点 南区数统楼406 报告人所属单位 湖北大学数学与统计学院 报告人职称/职务 教授，副院长 报告内容简介 An involution over finite fields is a permutation polynomial whose inverse is itself. Owing to this property, involutions over finite fields have been widely used in applications such as cryptography and coding theory. Following the idea in [1] to characterize the involutory behavior of the generalized cyclotomic mappings, gives a more concise criterion for $x^rh(x^s)\in \bF_q[x]$ being involutions over the finite field~$\bF_q$, where $r\geq 1$ and $s\,|\, (q-1)$. By using this criterion we propose a general method to construct involutions of the form $x^rh(x^s)$ over $\bF_q$ from given involutions over some subgroups of $\bF_q^*$ by solving congruent and linear equations over finite fields. Then, many classes of explicit involutions of the form $x^rh(x^s)$ over $\bF_q$ are obtained.

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