1- Consider the (7,4) Hamming code defined by the generator polynomial g(X) = 1 + X + X³ The codeword 0111001 is sent over a noisy channel, producing the received word 0101001 that has a single error. Determine the syndrome polynomial s(X) for this received word, and show that it is identical to the error polynomial e(X). 2- The generator polynomial of a (15, 11) Hamming code is defined by g(X) = 1 + X + X4 Develop the encoder and syndrome calculator for this code, using a systematic form for the code.

1- Consider the (7,4) Hamming code defined by the generator polynomial g(X) = 1 + X + X³ The codeword 0111001 is sent over a noisy channel, producing the received word 0101001 that has a single error. Determine the syndrome polynomial s(X) for this received word, and show that it is identical to the error polynomial e(X). 2- The generator polynomial of a (15, 11) Hamming code is defined by g(X) = 1 + X + X4 Develop the encoder and syndrome calculator for this code, using a systematic form for the code.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A: See attached file for a step by step explanation to find the required polynomial.

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Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Question

1- Consider the (7,4) Hamming code defined by the generator polynomial
g(X) = 1 + X + X³
The codeword 0111001 is sent over a noisy channel, producing the received word 0101001 that has
a single error. Determine the syndrome polynomial s(X) for this received word, and show that it is
identical to the error polynomial e(X).
2- The generator polynomial of a (15, 11) Hamming code is defined by
g(X) = 1 + X + X4
Develop the encoder and syndrome calculator for this code, using a systematic form for the code.

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