报告人：Sihem Mesnager教授

工作单位：巴黎第八大学

举办单位：数学学院

报告人简介：

Sihem Mesnager，教授，法国巴黎第八大学（数学系）和巴黎高等电信学校，主要研究领域涉及离散数学、对称密码学、编码理论等。IEEE信息理论法国分会主席、国际有限域算术学会组委会核心成员、曾任信息论国际顶级期刊《IEEE Transactions on Information Theory》编委、多个国际SCI期刊主编。在领域权威期刊发表论文170余篇，包括信息论国际顶级期刊、中国计算机学会和密码学会推荐A类期刊《IEEE Transactions on Information Theory》近50篇。因在密码学和编码学等研究领域的突出贡献，2020年荣获首届国际学术奖：乔治布尔奖（George Boole Prize）。

报告一：Functions-based codes over finite fields and their applications

报告时间：2024年9月21日（星期六）15:00-17:00

报告地点：ZOOM(房间号：941 5041 8339，密码：857993)

报告简介：

One of the leading research problems in coding theory is constructing new linear codes with appropriate parameters (functional in communication systems, consumer electronics and data storage systems), determining their weight distributions and studying their dual codes. This research also pays particular attention to applications. This talk concentrates on linear codes. We aim to present results and open questions by selecting families of linear codes over finite fields with arbitrary characteristics (some of them are designed for (toward) specific intended applications). Specifically, the emphasis will be on linear codes created from functions over finite fields. We shall discuss the advantages and limitations.

报告二：Interactions between maximally non-linear functions and linear codes

报告时间：2024年9月22日（星期日）15:00-17:00

报告地点：ZOOM(房间号：981 0482 7033，密码：298737)

报告简介：

Bent functions in an even characteristic are Boolean functions with the highest possible nonlinearity in an even number of variables. They were introduced by Rothaus and had been previously studied by Dillon and Rothaus less than five decades ago. Since 1974, bent functions have been extensively developed as interesting combinatorial objects and are significant in many mathematics-related areas for communications. In this talk, we discuss maximally nonlinear functions and their extensions as Hyperbent functions, a class of essential bent Boolean functions that achieve maximum distance from all bijective monomial functions and provide additional security against approximation attacks. They were initially proposed by Golomb and Gong in 1999 as components of substitution boxes (S-boxes) to ensure the security of symmetric cryptosystems. These functions were introduced in 2001 by Youssef and Gong for both theoretical and practical interest, using the concept of extended Walsh transform as a mathematical tool extending the classical Walsh Hadamard transform.

After an overview of these objects, our primary focus is their role in coding theory, first in the context of the covering radius of Reed-Muller codes and their interactions with cyclic codes based on idempotents elements.

报告三：(Cryptographic) Functions for Designing Locally Recoverable Codes in Distributed Storage

报告时间：2024年9月23日（星期一）15:00-17:00

报告地点：ZOOM(房间号：926 0048 6526，密码：554285)

报告简介：

There is a crucial need for highly scalable and reliable extensive data storage systems due to the rapid growth in data. Distributed storage systems (DSSs) store data on multiple distributed nodes and are widely used in file system storage, ample database storage, backup files, cloud storage, and more. The repair problem in DSSs is a key focus area.

Lately, there has been a notable increase in interest and focus on Locallyrecoverablecodes (LRCs), highlighting their growing importance in distributed storage systems. In this talk, we will explore function-based codes and present mathematical techniques for creating (optimal) LRCsfrom functions and polynomials. Notably, we emphasize the significant role of specific cryptographic functions in the design of LRCs.