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Module 6: Information Coding and Decoding

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Cyclic codes are represented using
(i) Frequency response
(ii) Generator polynomial
(iii) Trellis diagram
(iv) Fourier series

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Answer

Correct Option: (ii) Generator polynomial

Explanation

Cyclic codes (n,k)(n,k) are ideals in F2[x]/(xn−1)\mathbb{F}_2[x]/(x^n-1), generated by g(x)g(x) dividing xn−1x^n-1. Codewords c(x)=m(x)g(x)c(x)=m(x)g(x). Generator g(x)g(x) degree n−kn-k, parity check h(x)=(xn−1)/g(x)h(x)=(x^n-1)/g(x). Example Hamming (7,4) g(x)=x3+x+1g(x)=x^3+x+1.

Not frequency response, trellis, Fourier.

Final Answer

Generator polynomial → Option (ii).

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