11 papers
-Minimal Poset Codes
Jianhua Zheng, Yang Xu, Haibin Kan +2
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 +2
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-…
A Gröbner Basis Approach to Combinatorial Nullstellensatz
Yang Xu, Haibin Kan, Guangyue Han
In this paper, using some conditions that arise naturally in Alon's combinatorial Nullstellensatz as well as its various extensions and generalizations, we characterize Gröbner bas…
Isometries and MacWilliams Extension Property for Weighted Poset Metric
Yang Xu, Haibin Kan, Guangyue Han
Let be the cartesian product of a family of left modules over a ring , indexed by a finite set . We are concerned with the -weight on $\mathbf{H}…
Reflexivity of Partitions Induced by Weighted Poset Metric and Combinatorial Metric
Yang Xu, Haibin Kan, Guangyue Han
Let be the Cartesian product of a family of finite abelian groups. Via a polynomial approach, we give sufficient conditions for a partition of induced by…
Fourier-Reflexive Partitions Induced by Poset Metric
Yang Xu, Haibin Kan, Guangyue Han
Let be the cartesian product of a family of finite abelian groups indexed by a finite set . A given poset (i.e., partially ordered set) $\mathbf{P}=(Ω,\preccurlyeq_…
A Galois Connection Approach to Wei-Type Duality Theorems
Yang Xu, Haibin Kan, Guangyue Han
In , Wei proved a duality theorem that established an interesting connection between the generalized Hamming weights of a linear code and those of its dual code. Wei's dualit…