Generator matrix and parity check matrix of cyclic codes Generator matrix consists of algebraically independent subset of k codewords. These words can be words with weight of information part equal 1, i.e. words with information bits encoding integers: , in polynomial notation: . Then, following strategy of nonsystematic code encoding (7.1.17), code-base words can be designated:
That way, generator matrix of nonsystematic cyclic code can be obtained. Its rows, contain the generator polynomial shifted to the left by bits and supplemented by zeros.
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