Is c max a cyclic code, Is Cmax a cyclic code? Why? If yes, what is its generator, Other Engineering

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Is c max a cyclic code

Response to the following problem:

Let C₁ and C₂ denote two cyclic codes with the same block length n, with generator polynomials g₁(X) and g₂(X), and with minimum distances d₁ and d₂, respectively. Define C_max = C₁ ∪ C₂ and Cmin = C₁∩ C₂.

1. Is C_max a cyclic code? Why? If yes, what is its generator polynomial and its minimum distance?

2. Is C_min a cyclic code? Why? If yes, find its generator polynomial. What can you say about its minimum distance?

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