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Reversible codes have a range of wide applications in cryptography, data storage, and communication systems. In this paper, we investigated reversible codes under the Rosenbloom-Tsfasman metric (RT-metric). First, some properties of reversible codes in the RT-metric were described. An essential condition for a reversible code to be a maximum distance separable code (MDS code, in short) in the RT-metric was established. A necessary condition for a binary self-dual code to be reversible was proven and the same was generalized for q-ary self-dual reversible codes. Several constructions for reversible RT-metric codes were provided in terms of their generator matrices. [ABSTRACT FROM AUTHOR]

This paper deals with the study and construction of self-dual codes equipped with the Rosenbloom-Tsfasman metric (RT-metric, in short). An [s, k] linear code in the RT-metric over F q has codewords with k different non-zero weights. Using the generator matrix in standard form of a code in the RT-metric, the standard information set for the code is defined. Given the standard information set for a code, that for its dual is obtained. Moreover, using the basic parameters of a linear code, the covering radius and the minimum distance of its dual are also obtained. Eventually, necessary and sufficient conditions for a code to be self-dual are established. In addition, some methods for constructing self dual codes are proposed and illustrated with examples. [ABSTRACT FROM AUTHOR]

The notion of normality of codes in Hamming metric is extended to the codes in Rosenbloom-Tsfasman metric (RT-metric, in short). Using concepts of partition number and l-cell of codes in RT-metric, we establish results on covering radius and normality of q-ary codes in this metric. We also examine the acceptability of various coordinate positions of q-ary codes in this metric. And thus, by exploring the feasibility of applying amalgamated direct sum method for construction of codes, we analyze the significance of normality in RT-metric. [ABSTRACT FROM AUTHOR]