On Some Aspects Of Degenerated Cyclic Codes

Résumé

Degenerated cyclic codes constitute a fascinating area of study within coding theory, offering profound insights into the realm of algebraic structures and their applications in error detection and correction. In this work, we delve into various aspects of degenerated cyclic codes, aiming to provide a comprehensive understanding of their properties and significance. We begin by elucidating the fundamental concepts underlying cyclic codes and their degeneration, establishing a mathematical framework for analysis. Subsequently, we explore the algebraic structure of degenerated cyclic codes, investigating their generator and parity-check matrices, as well as their relationships with conventional cyclic codes. Moreover, we investigate the decoding algorithms tailored for degenerated cyclic codes, evaluating their efficiency and performance under different error conditions. Furthermore, we examine the applications of degenerated cyclic codes in practical scenarios, highlighting their utility in diverse domains such as telecommunications, storage systems, and cryptography. Through theoretical analysis and numerical simulations, we demonstrate the efficacy and versatility of degenerated cyclic codes, thereby emphasizing their significance in modern information theory. Overall, this study contributes to the advancement of coding theory by shedding light on the intricacies of degenerated cyclic codes and paving the way for future research endeavors in this burgeoning field.