Power Error Locating Pairs
release_iodgtzz5rfh27hjdi4wx5ue4ta
by
Alain Couvreur, Isabella Panaccione
2020
Abstract
We present a new decoding algorithm based on error locating pairs and
correcting an amount of errors exceeding half the minimum distance. When
applied to Reed–Solomon or algebraic geometry codes, the algorithm is a
reformulation of the so–called power decoding algorithm. Asymptotically,
it corrects errors up to Sudan's radius. In addition, this new framework
applies to any code benefiting from an error locating pair. Similarly to
Pellikaan's and Kötter's approach for unique algebraic decoding, our
algorithm provides a unified point of view for decoding codes with an algebraic
structure beyond the half minimum distance. It permits to get an abstract
description of decoding using only codes and linear algebra and without
involving the arithmetic of polynomial and rational function algebras used for
the definition of the codes themselves. Such algorithms can be valuable for
instance for cryptanalysis to construct a decoding algorithm of a code without
having access to the hidden algebraic structure of the code.
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