7 papers
Hyper-derivative Algebraic Geometry Codes via Local Expansions
Xiaofeng Liu, Hengfeng Liu, Jun Zhang +2
In this paper, we develop a systematic construction framework of hyper-derivative algebraic geometry codes via local expansions, extending hyper-derivative Reed-Solomon codes from…
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) have emerged as fundamental objects in modern coding theory, primarily due to their pivotal role in distributed and cloud storage systems. A major…
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,…
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…