Bounds for complexity of syndrome decoding for poset metrics

Marcelo Firer; Jerry Anderson Pinheiro

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arXiv · 1411.0724

Bounds for complexity of syndrome decoding for poset metrics

Marcelo Firer·Jerry Anderson Pinheiro

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Abstract

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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Marcelo Firer, Jerry Anderson Pinheiro. 2015-02-18. Bounds for complexity of syndrome decoding for poset metrics. https://arxiv.org/abs/1411.0724

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