RT-conjugate codes in the Rosenbloom-Tsfasman metric

Résumé

Linear Complementary Dual (LCD) codes are a special class of linear error-correcting code used in data transmission and storage. These codes possess specific algebraic properties that make them useful in applications, such as communication systems, cryptography, and data storage devices. These are particularly valuable in scenarios that require a high degree of error detection and correction. This study explores the characteristics of RT-conjugate codes within the Rosenbloom-Tsfasman metric (RT-metric). In this study, we focus on a specific subclass of LCD codes characterized by conjugate conditions. In particular, we establish sufficient conditions under which a linear code in the RT metric qualifies as an LCD code through its conjugate structure. We also analyzed the weight distribution of the dual of these codes in terms of their type and proposed several construction methods for RT-conjugate codes.