In
coding theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are stud ...
, a linear code is an
error-correcting code
In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea i ...
for which any
linear combination of
codewords is also a codeword. Linear codes are traditionally partitioned into
block code
In coding theory, block codes are a large and important family of error-correcting codes that encode data in blocks.
There is a vast number of examples for block codes, many of which have a wide range of practical applications. The abstract defini ...
s and
convolutional code
In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of th ...
s, although
turbo code
In information theory, turbo codes (originally in French ''Turbocodes'') are a class of high-performance forward error correction (FEC) codes developed around 1990–91, but first published in 1993. They were the first practical codes to closely ...
s can be seen as a hybrid of these two types. Linear codes allow for more efficient encoding and decoding algorithms than other codes (cf.
syndrome decoding
In coding theory, decoding is the process of translating received messages into codewords of a given code. There have been many common methods of mapping messages to codewords. These are often used to recover messages sent over a noisy channel, ...
).
Linear codes are used in
forward error correction
In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is ...
and are applied in methods for transmitting symbols (e.g.,
bit
The bit is the most basic unit of information in com