IJPAM: Volume 48, No. 2 (2008)

CODES SATISFYING THE CHAIN CONDITION
OVER ROSENBLOOM-TSFASMAN SPACES

Luciano Panek$^1$, Emerson Lazzarotto$^2$, Fernando Mucio Bando$^3$
$^{1,2,3}$Department of Mathematics
UNIOESTE - Universia Brasil - Universidade Estadual do Oeste do Paraná
1300, Av. Tarquínio Joslin dos Santos
Foz do Iguaçu - PR, CEP 85870-650, BRAZIL
$^1$e-mail: lucpanek@gmail.com


Abstract.Let $M_{n\times m}\left( \Bbb{F}_{q}\right) $ be the linear space of all $n\times m$ matrices over the finite field $\Bbb{F}_{q}$, equipped with the new weight introduced by Rosenbloom and Tsfasman. In this paper we extend the concept of generalized Wei weights for Rosenbloom-Tsfasman weights and show that all linear codes satisfy the chain condition in $M_{n\times 1}\left( \Bbb{F}_{q}\right) $.

Received: July 4, 2008

AMS Subject Classification: 94B05, 94B65

Key Words and Phrases: Rosenbloom-Tsfasman weight, generalized Hamming weights, chain condition

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 48
Issue: 2