Self-dual codes in Rosenbloom-Tsfasman metric

Abstract

This paper deals with the study and construction of self-dual codes equipped with Rosenbloom-Tsfasman metric (RT-metric, in short). An [s, k] linear code in RT-metric over Fq has codewords with k different non-zero weights. Using the generator matrix in standard form of a code in 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.