arXiv subjects

Yaozong Zhang

Publications and source records attributed to Yaozong Zhang.

3 recordsLinked to original sources

arXiv2026

Constructions of LCPs and LCD codes from twisted Reed-Solomon codes

Linear complementary pairs (LCPs) and linear complementary dual (LCD) codes have important applications in orthogonal direct-sum masking (ODSM), which provides effective countermeasures against side-channel attacks and fault-injection attacks. While LCD codes have been extensively investigated, comparatively fewer results are available for general LCPs. In this paper, we further investigate LCPs of twisted Reed--Solomon (TRS) codes. We derive necessary conditions for two TRS codes to form an LCP and establish several sufficient conditions and explicit constructions. We also study LCD codes constructed from TRS codes and investigate the security parameters of the resulting LCPs. Furthermore, under suitable conditions, we obtain MDS LCPs of TRS codes.

cs.IT↗

arXiv2025

Several new infinite families of NMDS codes with arbitrary dimensions supporting $t$-designs

Near maximum distance separable (NMDS) codes, where both the code and its dual are almost maximum distance separable, play pivotal roles in combinatorial design theory and cryptographic applications. Despite progress in fixed dimensions (e.g., dimension 4 codes by Ding and Tang \cite{Ding2020}), constructing NMDS codes with arbitrary dimensions supporting $t$-designs ($t\geq 2$) has remained open. In this paper, we construct two infinite families of NMDS codes over $\mathbb{F}_q$ for any prime power $q$ with flexible dimensions and determine their weight distributions. Further, two additional families with arbitrary dimensions over $\mathbb{F}_{2^m}$ supporting $2$-designs and $3$-designs, and their weight distributions are obtained. Our results fully generalize prior fixed-dimension works~\cite{DingY2024,Heng2023,Heng20231,Xu2022}, and affirmatively settle the Heng-Wang conjecture \cite{Heng2023} on the existence of NMDS codes with flexible parameters supporting $2$-designs.

cs.IT↗

arXiv2024

A new class of self-orthogonal linear codes and their applications

Self-orthogonal codes are a subclass of linear codes that are contained within their dual codes. Since self-orthogonal codes are widely used in quantum codes, lattice theory and linear complementary dual (LCD) codes, they have received continuous attention and research. In this paper, we construct a class of self-orthogonal codes by using the defining-set approach, and determine their explicit weight distributions and the parameters of their duals. Some considered codes are optimal according to the tables of best codes known maintained at \cite{Grassl} and a class of almost maximum distance separable (AMDS) codes from their duals are obtained. As applications, we obtain a class of new quantum codes, which are MDS or AMDS according to the quantum Singleton bound under certain conditions. Some examples show that the constructed quantum codes have the better parameters than known ones maintained at \cite{Bierbrauer}. Furthermore, a new class of LCD codes are given, which are almost optimal according to the sphere packing bound.

cs.IT↗