Linear Codes over $\mathbb{F}_{q}[u]/(u^s)$ with Respect to the Rosenbloom---Tsfasman Metric

Authors:
Mehmet Ozen;Irfan Siap
Affiliations:
Department of Mathematics, Sakarya University, Sakarya, Turkey;Adiyaman Education Faculty, Gaziantep University, Adiyaman, Turkey
Venue:
Designs, Codes and Cryptography
Year:
2006

Citing 7
Cited 1

Modular and p-adic cyclic codes

Designs, Codes and Cryptography
Applications of coding theory to the construction of modular lattices

Journal of Combinatorial Theory Series A
Maximum Distance Codes in Matn,s (Zk) with a Non-Hamming Metric and Uniform Distributions

Designs, Codes and Cryptography
Efficient decoding of Zpk-linear codes

IEEE Transactions on Information Theory
Type II codes over F2+uF2

IEEE Transactions on Information Theory
Cyclic codes and self-dual codes over F2+uF2

IEEE Transactions on Information Theory
Decoding of linear codes over Galois rings

IEEE Transactions on Information Theory

Cyclic codes over F2[u]/(u4- 1) and applications to DNA codes

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We investigate the structure of codes over$\mathbb{F}_q[u]/(u^s)$ rings with respect to the Rosenbloom-Tsfasman (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 define 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$\mathbb{F}_q[u]/(u^s)$ and show that all cyclic codes over$\mathbb{F}_q[u]/(u^s)$ rings are MDR. We propose a decoding algorithm for linear codes over these rings with respect to the RT metric.