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
## 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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