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
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
Hi-index | 0.00 |
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.