报告题目：On Four Conjectures of Heng-Ding and p-ary Linear Code…

报 告 人：施敏加

时 间：2026年5月8日 （周五）下午15:00-16:00

地 点：国交2号楼315会议室

简 介：Subfield codes of linear codes over finite fields have recently attracted great attention due to their wide applications in secret sharing schemes, authentication codes and association schemes. There are two major ingredients in this paper. The first ingredient is to solve four conjectures recently proposed by Heng and Ding (IEEE Trans. Inf. Theory, 68(6): 3643-3656, 2022). Besides, we also determine the weight distributions of subfield codes derived from $x^3$ and oval polynomials over $\F_{2^m}$. The second ingredient is to obtain two classes of p-ary linear codes from monomials over $\F_{p^m}$. We study the parameters of the constructed codes and determine their weight distributions. Notably, we show that the codes $\mathcal{C}_{(x^{p^i},p^m)}^{(p)}$ are optimal and almost optimal in many cases with respect to the online Database of Grassl. Finally, we observe that the derived linear codes also have the minimality property for most cases.

报告题目：几类经典代数编码的快速编码与译码算法设计

报 告 人：李宋宋

时 间：2026年5月8日 （周五）下午14:30-15:30

地 点：国交2号楼315会议室

简 介：代数编码广泛应用于数据存储、通信以及密码学，其核心问题在于如何在保证纠错能力的同时，实现低复杂度的编码与译码过程。本报告围绕几类经典代数编码的高效实现问题，介绍 Reed–Solomon（RS）码、Reed–Muller（RM）码以及代数几何（Algebraic Geometry, AG）码的快速编码与译码算法。报告以 RS 码为基础框架，利用其良好的代数结构，构建RM码及AG 码到 RS 码之间的高效变换，将RM码与AG码的编码与译码问题转化为相应RS码上的计算问题。报告将结合近期研究成果，介绍基于函数域自同构群的快速傅里叶变换技术以及RS码的拟线性时间编译码算法，任意阶RM 码的拟线性时间编译码算法，以及面向突发错误接近 Singleton 界的AG 码高效译码算法。

报告题目：Surface-Localized of Transmission Eigenfunctions in Sp…

报 告 人：张凯

时 间：2026年4月30日 （周四）下午15:30-16:30

地 点：国交2号楼315会议室

简 介：We present a comprehensive study of new discoveries on the spectral patterns of elastic transmission eigenfunctions, including boundary localization, surface resonance, and stress concentration. In the case where the domain is radial and the underlying parameters are constant, we give rigorous justifications and derive a thorough understanding of those intriguing geometric and physical patterns. We also derive sharp spectral density estimates establishing both lower and upper bounds to demonstrate that a significant proportion of transmission eigenfunctions manifest this surface-localizing behavior.