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• W2964397147 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 {em 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 Kotter'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." @default.
• W2964397147 created "2019-08-13" @default.
• W2964397147 creator A5063131196 @default.
• W2964397147 creator A5079112626 @default.
• W2964397147 date "2019-07-26" @default.
• W2964397147 modified "2023-09-25" @default.
• W2964397147 title "Power Error Locating Pairs" @default.
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• W2964397147 hasPublicationYear "2019" @default.
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