IJPAM: Volume 35, No. 2 (2007)

CHAIN CODES AND SPHERICAL TITS BUILDINGS

Luciano Panek$^1$, Marcelo Firer$^2$
$^1$State University of the West of the Paraná
Av. Tarquínio Joslin dos Santos 1300
Foz do Iguaçu, 85870-650, PR, BRAZIL
e-mail: lucpanek@gmail.com
$^2$State University of Campinas
Cx. Postal 6065, Campinas, 13081-970, SP, BRAZIL
e-mail: mfirer@ime.unicamp.br


Abstract.To an $n$-dimensional vector space $V$ over a finite field $\mathbf{F}_{q}$ there is an (naturally) associated spherical building of type $A_{n-1}$. The chambers of such a building are maximal flags: maximal sequences of nested subspaces of $V$. In the case $q=2$, there is a unique $\left( n-1\right) $-dimensional maximum distance separable code in $V$. We show the existence of chambers associated to such a code that are of chain type (in the sense of coding theory) and give a complete characterization of the connected components of the chain type chambers.

Received: December 12, 2006

AMS Subject Classification: 94B05, 14M15, 14NXX

Key Words and Phrases: Hamming weights, chain codes, spherical Tits buildings

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 35
Issue: 2