Question: Coding Theory in Math: PROBLEM 4. (i) Show that to + 1 is a factor of a - 1 in Za]. (ii) For all

Coding Theory in Math:

PROBLEM 4. (i) Show that " to + 1 is a factor of a" - 1 in Za]. (ii) For all prime numbers p, find a cyclic p-ary code of length 9 and dimension 2. Give the generator matrix and the parity check matrix of the code. Find its minimal distance. (You may leave negative numbers in polynomials and matrices to avoid writing the prime p.)

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