Luciano
Panek and Marcelo Firer,
*Chain Codes and Spherical Tits Buildings*

Abstract:

To a $n$-dimensional vector space $V$ over a finite field $\mathbb{F}_q$ it is possible to associate a structure of spherical Tits building. The chambers of such building are maximal flags: maximal sequences of nested subspaces. In the case $q=2$, there is a unique $( n-1) $-dimensional 1-MDS code $C\subset V$. We show the existence of chambers associated to such a code that are chain type (in the sense of codes theory) and given a complete characterization of the connected components of the chain type chambers.

Key words: Hamming weights, chain codes, spherical Tits buildings

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Abstract:

To a $n$-dimensional vector space $V$ over a finite field $\mathbb{F}_q$ it is possible to associate a structure of spherical Tits building. The chambers of such building are maximal flags: maximal sequences of nested subspaces. In the case $q=2$, there is a unique $( n-1) $-dimensional 1-MDS code $C\subset V$. We show the existence of chambers associated to such a code that are chain type (in the sense of codes theory) and given a complete characterization of the connected components of the chain type chambers.

Key words: Hamming weights, chain codes, spherical Tits buildings

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September 03, 2004