Codes over Galois rings with respect to the Rosenbloom-Tsfasman metric
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, vol.344, no.5, pp.790-799, 2007 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 344 Issue: 5
- Publication Date: 2007
- Doi Number: 10.1016/j.jfranklin.2006.02.001
- Journal Name: JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.790-799
- Yıldız Technical University Affiliated: No
Abstract
We investigate the structure of codes over Galois rings with respect to the Rosenbloom-Tsfasman (shortly RT) metric. We define a standard form generator matrix and show how we can determine the minimum distance of a code by taking advantage of its standard form. We compute the RT-weights of a linear code given with a generator matrix in standard form. We define maximum distance rank (shortly MDR) codes with respect to this metric and give the weights of the codewords of an MDR code. Finally, we give a decoding technique for codes over Galois rings with respect to the RT metric. (c) 2006 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.