报告题目 (Title)：行列比大于1/2的秩度量码的列表译码
List Decoding of Rank-Metric Codes with Row-To-Column Ratio Bigger Than 1/2
报告人 (Speaker)： 刘姝 副教授（电子科技大学）
报告时间 (Time)：2025年9月25日(周四) 15：00
报告地点 (Place)：腾讯会议 354 281 882
邀请人(Inviter)：丁洋
报告摘要：The main purpose of this paper is to explicitly construct a class of rank-metric codes C of rate R with the column-to-row ratio up to 2/3 and efficiently list decode these codes with decoding radius beyond the decoding radius (1 − R)/2 (note that (1 − R)/2 is at least half of relative minimum distance δ). In literature, the largest column-to-row ratio of rank-metric codes that can be efficiently list decoded beyond half of minimum distance is 1/2. Thus, it is greatly desired to efficiently design list decoding algorithms for rank-metric codes with the column-to-row ratio bigger than 1/2 or even close to 1. Our key idea is to compress an element of the field F_{q^m} into a smaller Fq-subspace via a linearized polynomial. Thus, the column-to-row ratio gets increased at the price of reducing the code rate. Our result shows that the compression technique is powerful and it has not been employed in the topic of list decoding of both the Hamming and rank metrics. Apart from the above algebraic technique, we follow some standard techniques to prune down the list. The algebraic idea enables us to pin down the message into a structured subspace of dimension linear in the number n of columns. This “periodic” structure allows us to pre-encode the message to prune down the list.