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Divya Acharya

Publications and source records attributed to Divya Acharya.

6 recordsLinked to original sources
arXiv2026

AMDS and quantum AMDS Constacyclic codes of length $4p^\varsigma $ over $\mathbb{F}_{{p}^{m}}$

This paper provides a comprehensive analysis of almost maximum distance separable (AMDS) constacyclic codes of length $4p^{\varsigma}$ over the finite field $\mathbb{F}_{p^m}$, where $p$ is an odd prime number. Furthermore, it introduces the construction of quantum AMDS (qAMDS) codes, drawing on the principles of the Calderbank-Shor-Steane (CSS) framework, which enhances their applicability in quantum error correction. This work aims to deepen the understanding of these codes and their potential uses in both classical and quantum computing environments.

math.CO↗
arXiv2026

Context-Aware Autoencoders for Anomaly Detection in Maritime Surveillance

The detection of anomalies is crucial to ensuring the safety and security of maritime vessel traffic surveillance. Although autoencoders are popular for anomaly detection, their effectiveness in identifying collective and contextual anomalies is limited, especially in the maritime domain, where anomalies depend on vessel-specific contexts derived from self-reported AIS messages. To address these limitations, we propose a novel solution: the context-aware autoencoder. By integrating context-specific thresholds, our method improves detection accuracy and reduces computational cost. We compare four context-aware autoencoder variants and a conventional autoencoder using a case study focused on fishing status anomalies in maritime surveillance. Results demonstrate the significant impact of context on reconstruction loss and anomaly detection. The context-aware autoencoder outperforms others in detecting anomalies in time series data. By incorporating context-specific thresholds and recognizing the importance of context in anomaly detection, our approach offers a promising solution to improve accuracy in maritime vessel traffic surveillance systems.

cs.CV↗
arXiv2025

Reversible and Reversible-Complement Double Cyclic Codes over F4+vF4 and its Application to DNA Codes

In this article, we study the algebraic structure of double cyclic codes of length $(m, n)$ over $\mathbb{F}_4$ and we give a necessary and sufficient condition for a double cyclic code over $\mathbb{F}_4$ to be reversible. Also, we determine the algebraic structure of double cyclic codes of length $(m, n)$ over $\mathbb{F}_4+v\mathbb{F}_4$ with $v^2=v$, satisfying the reverse constraint and the reverse-complement constraint. Then we establish a one-to-one correspondence $\psi$ between the 16 DNA double pairs $S_{D_{16}} $ and the 16 elements of the finite ring $\mathbb{F}_4+v\mathbb{F}_4$. We also discuss the GC-content of DNA double cyclic codes.

math.RA↗
arXiv2025

Lee Distance of cyclic codes of length $2^\varsigma$ over $\mathbb{F}_{2^m} + u\mathbb{F}_{2^m} + u^2\mathbb{F}_{2^m}$

Let $p$ be a prime number and $\varsigma$ and $m$ be a positive integers. Let $\mathcal{R} = \mathbb{F}_{2^m} + u\mathbb{F}_{2^m} + u^2\mathbb{F}_{2^m}$ ($u^3 = 0$). Cyclic codes of length $2^\varsigma$ over $\mathcal{R}$ are precisely the ideals of the local ring $\frac{\mathcal{R}[x]}{\langle x^{2^\varsigma}-1 \rangle}$. The Gray map from a code of Lee weight over $\mathbb{Z}_4$ to a code with Hamming weight over $\mathbb{F}_2$ is known to preserve weight. In this paper, we determine the Lee distance of cyclic codes of length $2^\varsigma$ over $\mathcal{R}$.

math.CO↗
arXiv2024

Repeated-Root Constacyclic Codes of Length $3p^s$ over the Finite Non-Chain Ring $\frac{\mathbb{F}_{p^m}[u, v]}{\langle u^2, v^2, uv-vu\rangle}$ and their Duals

This study aims to determine the algebraic structures of $\alpha$-constacyclic codes of length $3p^s$ over the finite commutative non-chain ring $\mathcal{R}=\frac{\mathbb{F}_{p^m}[u, v]}{\langle u^2, v^2, uv-vu\rangle}$, for a prime $p \neq 3.$ For the unit $\alpha$, we consider two different instances: when $\alpha$ is a cube in $\mathcal{R}$ and when it is not. Analyzing the first scenario is relatively easy. When $\alpha$ is not a unit in $\mathcal{R}$, we consider several subcases and determine the algebraic structures of constacyclic codes in those cases. Further, we also provide the number of codewords and the duals of $\alpha$-constacyclic codes.

math.CO↗