Codes over Galois rings with respect to the Rosenbloom-Tsfasman metric

Ozen, Mehmet; Siap, İrfan

doi:10.1016/j.jfranklin.2006.02.001

Codes over Galois rings with respect to the Rosenbloom-Tsfasman metric

Atıf İçin Kopyala

Ozen M., Siap I.

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, cilt.344, sa.5, ss.790-799, 2007 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 344 Sayı: 5
Basım Tarihi: 2007
Doi Numarası: 10.1016/j.jfranklin.2006.02.001
Dergi Adı: JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.790-799
Yıldız Teknik Üniversitesi Adresli: Hayır

Özet

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.