arXiv subjects

Chenlu Jia

Publications and source records attributed to Chenlu Jia.

3 recordsLinked to original sources

arXiv2026

Four classes of few-weight self-orthogonal codes and their applications for LCD codes and quantum codes

Since self-orthogonal codes, few-weight codes, linear complementary dual codes(LCD codes, for short) and quantum codes have nice applications in coding theory and cryptography, they have received continuous attention. In 2024, by introducing the notion of the augment code, Heng et al.[30] constructed several classes of few-weight self-orthogonal codes basing on defining sets, which are introduced by Ding et al.[10] in 2007. In this manuscript, for two classes of defining sets, we consider the corresponding augmented codes, construct a class of projective four-weight self-orthogonal codes and three classes of four-weight self-orthogonal codes. And for two classes of these four-weight self-orthogonal linear codes, we determine the parameters of their dual codes. As applications, we construct two classes of LCD codes and a class of quantum codes. In particular, we prove that there exists a class of these LCD codes whose dual codes are almost optimal LCD codes according to the sphere packing bound, and a class of quantum codes are AMDS according to the quantum Singleton bound.

cs.IT↗

arXiv2026

The Hermitian Hull Dimensions for a Class of (L,P)-Twisted Generalized Reed-Solomon Codes

Determining the hull of linear codes has long been an important topic in coding theory. Recently, non-generalized Reed-Solomon (in short, non-GRS) codes have attracted extensive research interest. The (L,P)-twisted generalized Reed-Solomon (in short, (L,P)-TGRS) code, which is an extension of the generalized Reed-Solomon (GRS) code, constitutes a well-studied calss of non-GRS codes.There are numerous works focusing on the Euclidean hull of (L,P)-TGRS codes, while only a few results on the Hermitian hull of (L,P)-TGRS codes. In this paper, we focus on a class of (L,P)-TGRS codes C_k(a). By taking a special class of the vector a with length i(q-1), and analyze the parity of i and the relation between i and q+1, we divide three cases to fully determine the Hermitian hull dimension of C_k(a). As an application, we construct two classes of entanglement-assisted quantum error-correcting codes.

cs.IT↗

arXiv2025

Multi-Twisted Generalized Reed-Solomon Codes: Structure, Properties, and Constructions

Maximum distance separable (in short, MDS), near MDS (in short, NMDS), and self-orthogonal codes play a pivotal role in algebraic coding theory, particularly in applications such as quantum communications and secret sharing scheme. Recently, the construction of non-generalized Reed-Solomon (in short, non-GRS) codes has emerged as a significant research frontier. This paper presents a systematic investigation into a generalized class of $(\mathcal{L}, \mathcal{P})$-twisted generalized Reed-Solomon (TGRS) codes characterized by $\ell$ twists, extending the structures previously introduced by Beelen et al. and Hu et al.. We first derive the explicit parity-check matrices for these codes by analyzing the properties of symmetric polynomials. Based on this algebraic framework, we establish necessary and sufficient conditions for the self-orthogonality of the proposed codes, generalizing several recent results. Leveraging these self-orthogonal structures, we construct new families of LCD MDS codes that offer greater flexibility in code length compared to existing literature. Furthermore, we provide a characterization of the NMDS property for these codes, offering a partial solution to the open problem concerning general $(\mathcal{L}, \mathcal{P})$-TGRS codes posed by Hu et al. (2025). Finally, we rigorously prove that these codes are of non-GRS type when $2k > n$, providing an improvement over previous bounds. Theoretical constructions are validated through numerical examples.

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