编码（Coding）中的术语

Linear combination

In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).

Linear code

In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword. Linear codes are traditionally partitioned into block codes and convolutional codes, although turbo codes can be seen as a hybrid of these two types.^[1] Linear codes allow for more efficient encoding and decoding algorithms than other codes (cf. syndrome decoding).

Parity-check matrix

The rows of a parity check matrix are the coefficients of the parity check equations.^[2] That is, they show how linear combinations of certain digits (components) of each codeword equal zero.

奇偶校验矩阵是奇偶校验等式的系数。

Syndrome decoding

syndrome decoding is  minimum distance decoding  using a reduced lookup table.