Original scientific paper

Self-dual codes in the Rosenbloom-Tsfasman metric

Venkatrajam Marka ; Department of Mathematics, National Institute of Technology Warangal, Warangal, India
R. S. Selvaraj ; Department of Mathematics, National Institute of Technology Warangal, Warangal, India
Irrinki Gnanasudha ; Department of Mathematics, National Institute of Technology Warangal, Warangal, India

Abstract

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 Fq 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.

Keywords

linear code; self-dual code; standard information set; covering radius; RTmetric

Hrčak ID:

176721

URI

https://hrcak.srce.hr/176721

Publication date:

4.4.2017.

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