Encoding operation

Using the elements of GF(24), the generator polynomial of the triple-errorvcorrecting Reed-Solomon code, RS(15, 9), is obtained. For the construction of GF(24), the primitive polynomial p(x) . x4 + x2 + 1 is used.

Assume that the dataword to be encoded is given as

d(x) = x8 + α6 x5 + α3 x2  + x + 1:

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Encode d(x), and let c(x) be the code-word obtained after encoding operation. The error pattern is given as

 e(x) = α2 x9 + α5+x4. Decode the received word polynomial

r (x) = c(x) + e(x). Use Berlekamp algorithm in your decoding operation.