10月31日:编码密码及相关数学理论研讨会
发布时间:2024-10-29 浏览量:10

报告一:MSR codes with linear field size and smallest sub-packetization for any number of helper nodes (胡思煌)

报告时间:2024年10月31日15:00-17:00

报告地点:理科大楼B1202

报告摘要:

The sub-packetization $\ell$ and the field size $q$ are of paramount importance in the MSR array code constructions. For optimal-access MSR codes, Balaji \emph{et al.} proved that $\ell\geq s^{\left\lceil n/s \right\rceil}$, where $s = d-k+1$. Rawat \emph{et al.} showed that this lower bound is attainable for all admissible values of $d$ when the field size is exponential in $n$. After that, tremendous efforts have been devoted to reducing the field size. However, till now, reduction to linear field size is only available for $d\in\{k+1,k+2,k+3\}$ and $d=n-1$.

   In this work, we construct the first class of explicit optimal-access MSR codes   with the smallest sub-packetization $\ell = s^{\left\lceil n/s \right\rceil}$ for all $d$ between $k+1$ and $n-1$, resolving an open problem in the survey (Ramkumar \emph{et al.}, Foundations and Trends in Communications and Information Theory: Vol. 19: No. 4). We further propose another class of explicit MSR code constructions (not optimal-access) with even smaller sub-packetization $s^{\left\lceil n/(s+1)\right\rceil }$ for all admissible values of $d$, making significant progress on another open problem in the survey. Previously, MSR codes with $\ell=s^{\left\lceil n/(s+1)\right\rceil }$ and $q=O(n)$ were only known for $d=k+1$ and $d=n-1$. The key insight that enables a linear field size in our construction is to reduce $\binom{n}{r}$ global constraints of non-vanishing determinants to $O_s(n)$ local ones, which is achieved by carefully designing the parity check matrices. This is a joint work with Guodong Li, Ningning Wang, and Min Ye.


报告人简介:

胡思煌,山东大学网络空间安全学院教授,目前主要研究方向是通信与存储编码理论。在组合数学与信息论期刊和会议上发表30余篇论文,主持国家重点研发计划青年科学家项目、基金委青年项目和CCF-华为胡杨林基金,指导博士生获2024 IEEE Jack Keil Wolf ISIT Student Paper Award。



报告二:Deep Holes of Twisted Reed-Solomon Codes (方伟军)

报告时间:2024年10月31日15:00-17:00

报告地点:理科大楼B1202

报告摘要:

The deep holes of a linear code are the vectors that achieve the maximum error distance to the code. There has been extensive research on the topic of deep holes in Reed-Solomon codes. In this talk, as a generalization of Reed-Solomon codes, we investigate the problem of deep holes in a class of twisted Reed-Solomon codes. The covering radius and a standard class of deep holes of twisted Reed-Solomon codes are obtained for a general evaluation set. Furthermore, we completely determine the deep holes of the full-length twisted Reed-Solomon codes with parameters in a certain range.


报告人简介:

方伟军,山东大学网络空间安全学院教授、博士生导师。2019年博士毕业于南开大学,导师为符方伟教授。 2019-2021年在清华大学从事博士后工作,导师为夏树涛教授。目前主要研究方向为代数编码、量子纠错码以及分布式存储编码等。在IEEE TIT、FFA、DCC以及ISIT等信息论与编码理论主流期刊与会议发表二十余篇论文。主持1项国家自然科学青年基金,作为学术骨干参与国家重点研发计划项目和青年科学家项目。获得山东大学齐鲁青年学者,入选山东省泰山学者青年专家人才计划。



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