arXiv subjects

Puyin Wang

Publications and source records attributed to Puyin Wang.

5 recordsLinked to original sources

arXiv2025

Non-Reed-Solomon Type MDS Codes from Elliptic Curves

New families of maximum distance separable (MDS) codes are constructed from elliptic curves by exploiting their group structures. In contrast to classical constructions based on divisors supported at a single rational point, the proposed approach employs divisors formed by multiple distinct points constituting a maximal subgroup of the curve. The resulting codes achieve parameters approaching the theoretical upper bound $(q + 1 + \lfloor 2\sqrt{q} \rfloor)/2$ and include non Reed-Solomon (RS) MDS codes. The inequivalence of these codes to RS codes is established through an explicit analysis on the rank of the Schur product of their generator matrices. These results extend the known parameter range of elliptic MDS codes and provide additional evidence supporting the tightness of existing upper bounds for algebraic geometry MDS codes.

cs.IT↗

arXiv2025

Column Twisted Reed-Solomon Codes as MDS Codes

In this paper, we study column twisted Reed-Solomon(TRS) codes. We establish some sufficient conditions for these codes to be MDS and show that the dimension of their Schur square codes is $2k$. Consequently, these TRS codes are shown to be not equivalent to Reed-Solomon(RS) codes. Moreover, our construction offers more flexible parameters than existing twisted generalized Reed-Solomon(TGRS) code designs. For a large odd prime power $q$, systematically constructed TGRS codes are known to be limited to length $\frac{q+1}{2}$. By contrast, our column TRS construction supports code lengths up to $\frac{q+3}{2}$. Finally, we present the dual codes of column TRS codes. Overall, this work introduces a new method for constructing MDS codes by appending column vectors to some generator matrix of an RS code.

cs.IT↗

arXiv2025

A Generic Construction on Self-orthogonal Algebraic Geometric Codes and Its Applications

In the realm of algebraic geometric (AG) codes, characterizing dual codes has long been a challenging task. In this paper we introduces a generalized criterion to characterize self-orthogonality of AG codes based on residues, drawing upon the rich algebraic structures of finite fields and the geometric properties of algebraic curves. We also present a generic construction of self-orthogonal AG codes from self-dual MDS codes. Using these approaches, we construct several families of self-dual and almost self-dual AG codes. These codes combine two merits: good performance as AG code whose parameters are close to the Singleton bound together with Euclidean (or Hermtian) self-dual/self-orthogonal property. Furthermore, some AG codes with Hermitian self-orthogonality can be applied to construct quantum codes with notably good parameters.

cs.IT↗

arXiv2025

Self-orthogonal and self-dual codes from maximal curves

In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing algebraic structure of finite fields and geometric properties of algebraic curves. Moreover, we construct self-orthogonal and self-dual codes with parameters $[n, k, d]_{q^2}$ satisfying $k + d$ is close to $n$. Additionally, quantum codes with large minimum distance are also constructed.

cs.IT↗

arXiv2024

Two Classes of Quantum MDS Codes with Large Minimal Distance

In this paper, two classes of quantum MDS codes are constructed. The main tools are multiplicative structures on finite fields. Carefully choosing different cosets can make the corresponding generalized Reed-Solomon codes Hermitian self-orthogonal, which yields quantum MDS codes by utilizing Hermitian type CSS construction. In some cases, these codes have minimal distances larger than $q/2$. Also, the parameters of these codes have never been reported before.

cs.IT↗