[Solved] Let Q 7 T 3 Choose 3 Find Generator Polynomial G X Generator Matrix New Reed Solomon Code Q37193098

I. Let q = 7 and t = 3. Choose a = 3. (a) Find the generator polynomial g(x) and the generator matrix for the new Reed Solomon code. b) What are n, k, d c)Encode the data (1, 2, 1,0) (d) You receive the codeword (5, 1,1,3,0,0). What is the data? (e) You receive the codeword (3, 0,5,2,0,0). Show that an error occurred. If exactly one error occurred, find the data. Review: Reed-Solomon code as a BCH code Choose a generator of F: Let N = q-1. Choose t such that 2 <t < N and let K = N-t + l so that K-12 K 1. Choose the generator polynomial g(x) e Falrl to be the polynomial of degree t-1 having roots a’ for 1 sist 1. Codewords are coefficients of polynomials of degree s N-1 which are multiples of g(x). Equivalently, (co-, ., c#1) codeword iff ai root for l i < N-K of 0 if and only if error. Polynomial division by g(x) has remainder r(x) The minimal distance D 2 t Show transcribed image text I. Let q = 7 and t = 3. Choose a = 3. (a) Find the generator polynomial g(x) and the generator matrix for the new Reed Solomon code. b) What are n, k, d c)Encode the data (1, 2, 1,0) (d) You receive the codeword (5, 1,1,3,0,0). What is the data? (e) You receive the codeword (3, 0,5,2,0,0). Show that an error occurred. If exactly one error occurred, find the data. Review: Reed-Solomon code as a BCH code Choose a generator of F: Let N = q-1. Choose t such that 2

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Answer to I. Let q = 7 and t = 3. Choose a = 3. (a) Find the generator polynomial g(x) and the generator matrix for the new Reed S… . . .