Questions. 7.1 What are the key parameters of Hamming codes?

7.1 What are the key parameters of Hamming codes?

7.2 What are the advantages of cyclic codes?

7.3 Is it possible to use Hamming codes and cyclical codes for correction of single errors? What will parameters of these codes be?

Tasks

7.1 The generator matrix of a code (7, 4) is set:

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Define the allowed code word of this code b if word of simple code on encoder input a = (1110) is set.

7.2 The parity check matrix of a code (7, 4) is set:

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Give a functional chart of the decoder of this code.

7.4 Consider an example of formation of a allowed code word if a word of a simple code is a = (10010).

7.5 By analogy to an example of section 7.1 make the table of Hamming codes parameters for values r = 2, 3, 4. As these codes have identical minimum distance, compare them on suitability for realization in practical systems. Formulate the recommendation and a substantiation of application of the best (in your opinion) code from this list.

7.6 For Hamming code recommended in the previous section, form generator and parity check matrixes.

7.7 By the rules stated in Exercise 4.1 define value of minimum distance by a generator matrix of code from the Task 7.5.