Questions. 5.1 What kind will a matrix of double errors have?

5.1 What kind will a matrix of double errors have? How will it change in comparison with a matrix of single errors (5.11)?

5.2 How are parameters of binary syndrome representation (see table 5.1) connected with general number of possible configurations variants which detected and corrected errors by syndrome decoding?

5.3 How will the syndrome format change if to apply a method of syndrome decoding to decoding double errors?

5.4 Give the generalized block diagram of syndrome decoder of a block (n, k) code. What is the function of syndrome analyzer?

Tasks

5.1 By the principles stated in the Example 5.1 represent structure a systematic block code intended for detection of double errors with the generating matrix (4.6).

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

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

5.3 Define code distance of a code (7, 4) with a generator matrix from the Task 5.2.

5.4 Represent a encoder structure of a code (7, 4) with the same generator matrix.