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Encyclopedia of Cryptography and Security pp 319–322Cite as

Decoding Algorithms

  • Reference work entry

  • 263 Accesses

Synonyms

Error-correction decoding; List decoding

Related Concepts

Berlekamp–Massey Algorithm; Code-Based Cryptography; Cyclic Codes; McEliece Public Key Cryptosystem; Niederreiter Encryption Scheme

Definition

A decoding algorithm for a linear code C over \({\mathbb{F}}_{q}\) receives a vector y in \({\mathbb{F}}_{q}^{n}\) and a positive integer w as inputs. The output is the set of all elements \(c \in C\) at distance at most w from y; the set is empty if there is no such c.

Background

Error-correcting codes are used to protect information which is sent over noisy channels. Instead of sending a message directly the corresponding codeword in an error-correcting code is sent over the channel. During this transmission some errors might occur. On the other end of the channel the receiver tries to retrieve the codeword by correcting those errors using a decoding algorithm. If the decoding process is successful the receiver can retrieve the original message from the codeword. The...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Christiane Peters

Authors
  1. Christiane Peters
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

  2. Center for Secure Information Systems, George Mason University, Fairfax, VA, 22030-4422, USA

    Sushil Jajodia

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Peters, C. (2011). Decoding Algorithms. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_382

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