Linear codes over F-q[u]/(u(s)) with respect to the Rosenbloom-Tsfasman metric


Ozen M., Siap I.

DESIGNS CODES AND CRYPTOGRAPHY, vol.38, no.1, pp.17-29, 2006 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 1
  • Publication Date: 2006
  • Doi Number: 10.1007/s10623-004-5658-5
  • Title of Journal : DESIGNS CODES AND CRYPTOGRAPHY
  • Page Numbers: pp.17-29

Abstract

We investigate the structure of codes over F-q[u]/(u(s)) rings with respect to the Rosenbloom-Tsfasman (RT) metric. We de. ne 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 de. ne MDR (maximum distance rank) codes with respect to this metric and give the weights of the codewords of an MDR code. We explore the structure of cyclic codes over F-q[u]/(u(s)) and show that all cyclic codes over F-q[u]/(u(s)) rings are MDR. We propose a decoding algorithm for linear codes over these rings with respect to the RT metric.