8 papers
When Do Subset Sums in Finite Abelian Groups Support -Designs?
Hengfeng Liu, Chunming Tang, Cuiling Fan +1
Subset sums over finite abelian groups lie at the intersection of additive combinatorics, design theory, and coding theory. Let be a finite abelian group, and let $\cB_k^x$ be…
Beyond Polynomials: Optimal Locally Recoverable Codes from Good Rational Functions
Hengfeng Liu, Sihem Mesnager, Chunming Tang +1
Locally recoverable codes (LRCs) play an important role in distributed and cloud storage systems. The celebrated Tamo--Barg construction of optimal LRCs is based on the notion of \…
Improved Penalty Function Approaches for Optimization Problems with General Orthogonality
Yongshen Zhang, Xin Liu, Nachuan Xiao +1
In this paper, we consider a class of generalized orthogonal optimization constraint problems (GOOCP) over , where the variable is restricted within th…
Rank Distribution and Dynamics of Gram Matrices from Binary m-Sequences with Applications to LCD Codes
Hengfeng Liu, Chunming Tang, Cuiling Fan +1
The Gram matrix is a classical object formed from the pairwise inner products of a collection of vectors, with fundamental roles in functional analysis, statistics, combinatorics,…
The Asymmetric Hamming Bidistance and Distributions over Binary Asymmetric Channels
Shukai Wang, Cuiling Fan, Chunming Tang +1
The binary asymmetric channel is a model for practical communication systems where the error probabilities for symbol transitions and differ substa…
Capacity-Achieving Codes for Noisy Insertion Channels
Hengfeng Liu, Chunming Tang, Cuiling Fan
DNA storage has emerged as a promising solution for large-scale and long-term data preservation. Among various error types, insertions are the most frequent errors occurring in DNA…
A Generic Construction of -ary Near-MDS Codes Supporting 2-Designs with Lengths Beyond
Hengfeng Liu, Chunming Tang, Zhengchun Zhou +2
A linear code with parameters is called maximum distance separable (MDS), and one with parameters is called almost MDS (AMDS). A code is near-MD…
Combinatorial -Designs from Finite Abelian Groups and Their Applications to Elliptic Curve Codes
Hengfeng Liu, Chunming Tang, Cuiling Fan +1
In this paper, we establish the conditions for some finite abelian groups and the family all the -sets in each of them summing up to an element to form -designs. We fully…