Multiplication Table of GF(8)

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Thank u, sir! Without these details wud not have understood those online Galois calculators .

donitarose
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In error correction, why do we shift the entries of a matrix. What has this got to do with CRC. For example, is a is alpha, the first row is a^n-1 ... a^2 a 1 0. The second row is a^n...a^3 a^2 a 1 0 and so on? How can the last column of this matrix become parity or check bits?

mohammadhaq
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in GF(8), 2*4 = 8 mod 8 = 0 ? but in the table it is written as 3, then it becomes GF(5) right ?

tarunmnair