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Merge pull request #116 from sp5wwp/main 

Italic g(x)
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Wojciech Kaczmarski 2022-07-14 18:12:13 +02:00 committed by GitHub
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pages/04.appendix/04.golay-encoder/docs.md
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#### Extended Golay(24,12) code
The extended Golay(24,12) encoder uses generating polynomial g given below to generate the 11 check bits. The check bits and an additional parity bit are appended to the 12 bit data, resulting in a 24 bit codeword. The resulting code is systematic, meaning that the input data (message) is embedded in the codeword.
The extended Golay(24,12) encoder uses generating polynomial *g(x)* given below to generate the 11 check bits. The check bits and an additional parity bit are appended to the 12 bit data, resulting in a 24 bit codeword. The resulting code is systematic, meaning that the input data (message) is embedded in the codeword.
\(g(x) = x^{11} + x^{10} + x^6 + x^5 + x^4 + x^2 + 1\)