Reference Work Entry

Encyclopedia of Cryptography and Security

pp 319-322

Decoding Algorithms

  • Christiane PetersAffiliated withDepartment of Mathematics and Computer Science, Technische Universiteit Eindhoven


Error-correction decoding; List decoding

Related Concepts

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


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.


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 mess ...

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