The encoding used for machine language is

Binary coding generally refers to linear grouping coding                                                                                                                                                                                                                          k] linear block code is to divide the information into a segment of k symbols (called an information group), and turn it into a group of n symbols in length through the encoder, as a [n, k] linear block code Codeword. If there are q values ​​for each code element (q is a prime power, base q), then there are a total of q kth power codewords.

When the relationship between the information symbol and the supervision symbol of the block code is a linear relationship (connected by a system of linear equations), this block code is called a linear block code. Including Hamming code and cyclic code.

For a binary linear block code of length n, it has possible codewords, from which M= codewords (k

In linear block codes, the number of different digits on the corresponding bits of two code words is called code word distance, referred to as distance, also known as Hamming distance.

The minimum value of the distance between each codeword in the encoding is called the minimum code distance d. The minimum code distance is the basis for measuring the error detection and correction capabilities of the code group. The relationship is as follows:

( 1) In order to detect e error codes, the minimum code distance d>e 1;

is required (2) In order to correct t error codes, the minimum code distance d>2t 1;

## is required #(3) In order to correct t error codes and detect e error codes at the same time, the minimum code distance d>e t 1,e>t is required.

Linear block codes are based on algebraic group theory. Each set of codewords constitutes a group in algebra. Their main properties are as follows:

(1) The sum of any two allowed codewords (for binary codes, the meaning of this sum is modulo two sums) is still a required codeword, that is to say, the linear block code has closed properties;

(2) The minimum code distance between codewords is equal to the minimum code weight of non-zero codes.

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