In this question we will go through an example of error-correcting codes. Since

Question

In this question we will go through an example of error-correcting codes. Since we will do this by hand, the message we will send is going to be short, consisting of n = 3 numbers, each modulo 5, and the number of errors will be k = 1. Your task is to construct the message. Let a0 = 4 and a1 = 3, a2 = 2; then use the polynomial interpolation formula to construct a polynomial P(x) of degree 2 (remember that all arithmetic is mod 5) so that P(0) = a0, P(1) = a1, and P(2) = a2; then extend the message to length N +2k by adding P(3) and P(4). What is the polynomial P(x) and what are P(3) and P(4)?

Explanation / Answer

Follow this link : http://www-inst.eecs.berkeley.edu/~cs70/fa12/hw/hw06_solutions.pdf

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