arXiv subjects

Biplab Chatterjee

Publications and source records attributed to Biplab Chatterjee.

6 recordsLinked to original sources

arXiv2026

Function-Based Minimal Linear Codes over Galois Rings $\mathrm{GR}(p^{n}, \ell)$: Minimality Criteria and Infinite Constructions

In this paper, we extend a necessary and sufficient condition for a linear code over a Galois ring to be minimal and establish new bounds on the length of an $m$-dimensional minimal linear code. Building upon this structural characterization, we further generalize the function-based minimality criteria introduced by Wu \emph{et al.} (Cryptogr. Commun. 14, 875-895, 2022) from the finite field setting to the framework of Galois rings. The transition from fields to rings introduces substantial algebraic challenges due to the presence of zero divisors and the richer module structure of $\mathrm{GR}(p^{n},\ell)$. By exploiting Frobenius duality and the chain structure of Galois rings, we derive refined necessary and sufficient conditions ensuring that linear codes arising from functions over $\mathrm{GR}(p^{n},\ell)$ are minimal. As an application of these criteria, we construct several infinite families of minimal linear codes over Galois rings, thereby significantly generalizing the constructions of Wu \emph{et al.} to the ring setting. Our results provide a unified framework that connects minimality theory, module duality over Frobenius rings, and function-based code constructions.

cs.IT↗

arXiv2025

Soft Computing Tools To Predict Varied Weight Components, Material and Tribological Properties of Al2219-B4C-Gr

Soft computing tools emerged as most reliable alternatives of traditional regression and statistical methods. In recent times, these tools can predict the optimum material compositions, mechanical and tribological properties of composite materials accurately without much experiment or even without experiment. In the present study, soft computing tools like fuzzy logic, Decision tree, genetic algorithms are employed to predict the reinforcement weight percentage of B4C(Boron Carbide) and Graphite(Gr) along with Aluminum (matrix material) weight percentage for Al2219 with B4C and graphite. The optimized material and tribological properties of Al2219 were also predicted using NSGA II genetic algorithms for multi-objective optimization. It is found that the predictions are at par with earlier ANN (artificial neural network) studies and experimental findings. It can be inferred that inclusion B4C has more impact on enhancement of mechanical properties as well as wear strength compared to Gr.

cs.CE↗

arXiv2025

LogSyn: A Few-Shot LLM Framework for Structured Insight Extraction from Unstructured General Aviation Maintenance Logs

Aircraft maintenance logs hold valuable safety data but remain underused due to their unstructured text format. This paper introduces LogSyn, a framework that uses Large Language Models (LLMs) to convert these logs into structured, machine-readable data. Using few-shot in-context learning on 6,169 records, LogSyn performs Controlled Abstraction Generation (CAG) to summarize problem-resolution narratives and classify events within a detailed hierarchical ontology. The framework identifies key failure patterns, offering a scalable method for semantic structuring and actionable insight extraction from maintenance logs. This work provides a practical path to improve maintenance workflows and predictive analytics in aviation and related industries.

cs.LG↗

arXiv2025

Reinforcement Learning for Self-Healing Material Systems

The transition to autonomous material systems necessitates adaptive control methodologies to maximize structural longevity. This study frames the self-healing process as a Reinforcement Learning (RL) problem within a Markov Decision Process (MDP), enabling agents to autonomously derive optimal policies that efficiently balance structural integrity maintenance against finite resource consumption. A comparative evaluation of discrete-action (Q-learning, DQN) and continuous-action (TD3) agents in a stochastic simulation environment revealed that RL controllers significantly outperform heuristic baselines, achieving near-complete material recovery. Crucially, the TD3 agent utilizing continuous dosage control demonstrated superior convergence speed and stability, underscoring the necessity of fine-grained, proportional actuation in dynamic self-healing applications.

cs.LG↗

arXiv2024

Generalization the parameters of minimal linear codes over the ring $\mathbb{Z}_{p^l}$ and $\mathbb{Z}_{{p_1}{p_2}}$

In this article, We introduce a condition that is both necessary and sufficient for a linear code to achieve minimality when analyzed over the rings $\mathbb{Z}_{n}$.The fundamental inquiry in minimal linear codes is the existence of a $[m,k]$ minimal linear code where $k$ is less than or equal to $m$. W. Lu et al. ( see \cite{nine}) showed that there exists a positive integer $m(k;q)$ such that for $m\geq m(k;q)$ a minimal linear code of length $m$ and dimension $k$ over a finite field $\mathbb{F}_q$ must exist. They give the upper and lower bound of $m(k;q)$. In this manuscript, we establish both an upper and lower bound for $m(k;p^l)$ and $m(k;p_1p_2)$ within the ring $\mathbb{Z}_{p^l}$ and $\mathbb{Z}_{p_1p_2}$ respectively.

cs.IT↗

arXiv2023

Structure and Construction of Two-Dimensional Minimal Linear Codes over the rings $\mathbb{Z}_{p^n}$ with Applications to Secret Sharing

Minimal linear codes play an important role in coding theory and cryptography, particularly in the construction of secret sharing schemes. In this paper, we investigate the structure and construction of two-dimensional minimal linear codes over the finite rings $\mathbb{Z}_{p^n}$. We provide an explicit construction of a family of two-dimensional linear codes generated by a structured $2\times m$ matrix over $\mathbb{Z}_{p^n}$ and prove that these codes are minimal whenever the generator matrix contains all $p^n+p^{n-1}$ essential types of column vectors. We further show that this condition is necessary: removing any of these column types destroys the resulting code's minimality. As a consequence, we establish a lower bound on the length of two-dimensional minimal linear codes over $\mathbb{Z}_{p^n}$. Several examples are presented to illustrate the construction and to verify the theoretical results. We also demonstrate that the proposed construction cannot be extended in a straightforward manner to rings of the form $\mathbb{Z}_{p^n q^l}$. Finally, we apply our results to the design of secret sharing schemes derived from minimal linear codes over $\mathbb{Z}_{p^n}$ and analyze the corresponding access structures. Our study highlights structural differences between minimal codes defined over finite rings and those over finite fields, revealing new perspectives for coding-theoretic constructions in cryptographic applications.

cs.IT↗