偏序集度量的综合征解码复杂度的界

2015 IEEE Information Theory Workshop (ITW) Pub Date : 2014-11-03 DOI:10.1109/ITW.2015.7133130

Marcelo Firer, Jerry Anderson Pinheiro

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引用次数: 4

摘要

在这项工作中，我们展示了如何分解线性码相对于任何给定的偏置度量。我们证明了综合征解码的复杂度是由一个极大的(初等)分解决定的，然后证明了一个偏阶的细化导致初等分解的细化。利用这一点，并考虑到已有的关于层次偏序集的结果，我们可以建立相对于偏序集度量的综合征解码复杂性的上界和下界。

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Bounds for complexity of syndrome decoding for poset metrics

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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2015 IEEE Information Theory Workshop (ITW)

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