1. Canonical- systematic form for codes in hierarchical poset metrics
- Author
-
Luciano Vianna Felix and Marcelo Firer
- Subjects
Discrete mathematics ,Algebra and Number Theory ,Computer Networks and Communications ,Direct sum ,Hamming bound ,Applied Mathematics ,Linear space ,Data_CODINGANDINFORMATIONTHEORY ,Microbiology ,Metric (mathematics) ,Isometry ,Discrete Mathematics and Combinatorics ,Generator matrix ,Partially ordered set ,Decoding methods ,Computer Science::Information Theory ,Mathematics - Abstract
In this work we present a canonical-systematic form of a generator matrix for linear codes whith respect to a hierarchical poset metric on the linear space $\mathbb F_q^n$. We show that up to a linear isometry any such code is equivalent to the direct sum of codes with smaller dimensions. The canonical-systematic form enables to exhibit simple expressions for the generalized minimal weights (in the sense defined by Wei), the packing radius of the code, characterization of perfect codes and also syndrome decoding algorithm that has (in general) exponential gain when compared to usual syndrome decoding.
- Published
- 2012