8 papers · 1 filter
-Minimal Poset Codes
Jianhua Zheng, Yang Xu, Haibin Kan +1
In this paper, we propose and study -minimal codes with respect to -support, where is a poset defined on the coordinate se…
Generalized Rank Weight and Extended Generalized Poset Weight Defined For Codes Over Rings: A Galois Connection Approach
Jianhua Zheng, Yang Xu, Haibin Kan +1
In this paper, we study generalized rank weights (GRWs) and extended generalized poset weight (EGPWs) of codes over rings via a Galois connection approach. First, we show that vari…
List-Decoding Counterexamples Yield Lower Bounds on Mutual Correlated Agreement Error
Yiwen Gao, Hong Yang, Yang Xu +1
Mutual correlated agreement captures whether a random linear combination of received words can create a new large agreement with a code, a property relevant to the soundness of bat…
An Elementary Approach to MacWilliams Extension Property and Constant Weight Code with Respect to Weighted Hamming Metric
Yang Xu, Haibin Kan, Guangyue Han
In this paper, we characterize the MacWilliams extension property (MEP) and constant weight codes with respect to -weight defined on via an elementary approach, w…
Reflexive Partitions Induced by Rank Support and Non-Reflexive Partitions Induced by Rank Weight
Yang Xu, Haibin Kan, Guangyue Han
In this paper, we study partitions of finite modules induced by rank support and rank weight. First, we show that partitions induced by rank support are mutually dual with respect…
-Minimal Codes with Respect to Rank Metric
Yang Xu, Haibin Kan, Guangyue Han
In this paper, we propose and study -minimal codes, a natural extension of minimal codes which have been extensively studied with respect to Hamming metric, rank metric and sum-…