Self-dual codes in Rosenbloom-Tsfasman metric

Venkatrajam Marka; R.S. Selvaraj; Irrinki Gnanasudha

Vol. 22 No. 1 (2017)

Regular Articles

Self-dual codes in Rosenbloom-Tsfasman metric

Published 2016-10-17

Venkatrajam Marka
R.S. Selvaraj
Irrinki Gnanasudha

Venkatrajam Marka
National Institute of Technology Warangal

R.S. Selvaraj
National Institute of Technology Warangal

Irrinki Gnanasudha
National Institute of Technology Warangal

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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.

Keywords

linear code, self-dual code, standard information set, covering radius, RT-metric

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Author Biography

Venkatrajam Marka

Department of Mathematics

R.S. Selvaraj

Assistant Professor,

Department of Mathematics

Irrinki Gnanasudha

Department of Mathematics