Maximum distance separable (MDS) codes are a type of error-correcting codes that aim to optimize the shortest possible distance between codewords. These codes are useful in situations where error correction is critical, such as data storage or communication systems, and they can be found in a variety of domains, including information theory, cryptography, and reliable data transmission. The concept of MDS codes is fundamental in designing robust and efficient error-correcting codes that can withstand the challenges posed by noisy communication channels or unreliable storage systems. The Rosenbloom-Tsfasman (RT) metric provides a framework for constructing codes optimized for error correction, and reversible codes leverage this to maximize their error-correction capabilities. This study explored the characteristics of reversible MDS codes in the RT-metric by analyzing the structure of different types of generator matrices. It also established various properties of these codes, such as the conditions under which certain reversible MDS codes were self-dual over $ \mathbb{F}_2 $ and $ \mathbb{F}_q $. In addition, this study proposed several constructions for reversible MDS codes in the RT-metric.
Citation: Bodigiri Sai Gopinadh, Venkatrajam Marka. Construction of reversible MDS codes in the Rosenbloom-Tsfasman metric[J]. AIMS Mathematics, 2025, 10(10): 24240-24256. doi: 10.3934/math.20251074
Maximum distance separable (MDS) codes are a type of error-correcting codes that aim to optimize the shortest possible distance between codewords. These codes are useful in situations where error correction is critical, such as data storage or communication systems, and they can be found in a variety of domains, including information theory, cryptography, and reliable data transmission. The concept of MDS codes is fundamental in designing robust and efficient error-correcting codes that can withstand the challenges posed by noisy communication channels or unreliable storage systems. The Rosenbloom-Tsfasman (RT) metric provides a framework for constructing codes optimized for error correction, and reversible codes leverage this to maximize their error-correction capabilities. This study explored the characteristics of reversible MDS codes in the RT-metric by analyzing the structure of different types of generator matrices. It also established various properties of these codes, such as the conditions under which certain reversible MDS codes were self-dual over $ \mathbb{F}_2 $ and $ \mathbb{F}_q $. In addition, this study proposed several constructions for reversible MDS codes in the RT-metric.
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Bodigiri Sai Gopinadh, Venkatrajam Marka. Construction of reversible MDS codes in the Rosenbloom-Tsfasman metric[J]. AIMS Mathematics, 2025, 10(10): 24240-24256. doi: 10.3934/math.20251074
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