报告题目： On Deep Holes of non-Reed-Solomon Codes
报告人：周海燕
邀请人：罗荣
讲座时间：2026年2月5日（星期四）下午15:00-16:00
讲座地点：犀浦校区7号教学楼X7510会议室
报告摘要：Let the linear code C(D, u, k) of length n and dimension k over F_q be defined as C(D, u, k) ={ (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) = { f(x) = \sum_{i=0}^{k-2} a_i x^i + a_k x^k \mid a_i \in \mathbb{F}_q }. 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.
报告人简介：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。