# 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} }

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.

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#### 2 Citations

The packing radius of a code and partitioning problems: The case for poset metrics

- Computer Science, Mathematics
- 2014 IEEE International Symposium on Information Theory
- 2014

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

- Computer Science
- 2018

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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