On Deep Holes of non-Reed-Solomon Codes
报告专家：周海燕 教授（南京师范大学）
报告时间：2月6日（周五）10:00-11:00
报告地点：四川大学数学学院西303
报告摘要：
Let the linear code $C(D, u, k)$ of length $n$ and dimension $k$ over $\mathbb{F}_q$ be defined as\[C(D, u, k) = \left\{ (u_1 f(\alpha_1), u_2 f(\alpha_2), \dots, u_n f(\alpha_n)) \mid f(x) \in S_k(x) \right\},\] with \[S_k(x) = \left\{ f(x) = \sum_{i=0}^{k-2} a_i x^i + a_k x^k \mid a_i \in \mathbb{F}_q \right\}.\] The code $C(D, u, k)$ is monomially equivalent to a twisted generalized Reed--Solomon code for $6 \leq 2k \leq n$ and $(p, k) = 1$. In this report, suppose $2 \leq k \leq n$, we determine the covering radius of $C(D, k)$ and study the deep hole of $C(D, u, k)$ for the case $u = 1$, denoted by $C(D, k)$. We completely determine the deep hole of $C(D, k)$ except the case $k = q - 4$ and $q = 2^m \geq 8$.
专家简介：
周海燕，南京师范大学数学科学学院教授，博士生导师，从事代数数论及其应用方面的研究，已在J. Number Theory, Acta Arith., J. Pure Appl. Algebra, Finite Fields and Their Appl.等杂志上发表论文三十多篇，主持国家自然科学基金项目5项。
邀请人：洪绍方