Bounds for complexity of syndrome decoding for poset metrics

@article{Firer2015BoundsFC,
  title={Bounds for complexity of syndrome decoding for poset metrics},
  author={M. Firer and J. A. Pinheiro},
  journal={2015 IEEE Information Theory Workshop (ITW)},
  year={2015},
  pages={1-5}
}
  • M. Firer, J. A. Pinheiro
  • Published 2015
  • Mathematics, Computer Science
  • 2015 IEEE Information Theory Workshop (ITW)
In this work we show how to decompose a linear code relatively to any given poset metric. We prove that the complexity of syndrome decoding is determined by a maximal (primary) such decomposition and then show that a refinement of a partial order leads to a refinement of the primary decomposition. Using this and considering already known results about hierarchical posets, we can establish upper and lower bounds for the complexity of syndrome decoding relatively to a poset metric. 
2 Citations
The packing radius of a code and partitioning problems: The case for poset metrics
TLDR
This work shows, without any restriction on the poset, that the relation between the weight and the packing radius of a vector is equivalent to a generalization of the classical partition problem. Expand
The General Case: Dead Ends and Hidden Passages
TLDR
This chapter explores some topics that are studied concerning coding with general poset metrics, with no restrictions on the poset, and the problems are difficult. Expand

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