The correct answer is A. 1, 2, 3, 4.
The steps involved in the decoding process of a cyclic code are as follows:
- Syndrome determination after the division of r(x) & g(x)
The syndrome is a number that is calculated by dividing the received code word $r(x)$ by the generator polynomial $g(x)$. The syndrome is a measure of the error that has occurred in the code word.
- Addition of error pattern to received code word
The error pattern is a binary sequence that is calculated from the syndrome. The error pattern is added to the received code word to correct the errors.
- Selection of error pattern corresponding to the syndrome
The error pattern is selected from a table of error patterns that is associated with the generator polynomial. The error pattern that is selected is the one that, when added to the received code word, results in a code word that is a multiple of the generator polynomial.
- Preparation of table comprising error patterns and syndromes
The table of error patterns and syndromes is a table that lists all of the possible error patterns and the corresponding syndromes. The table is used to select the correct error pattern to correct the errors in the received code word.
In the given question, the correct sequence of steps necessary for the correction of errors is as follows:
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Syndrome determination after the division of r(x) & g(x)
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Addition of error pattern to received code word
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Selection of error pattern corresponding to the syndrome
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Preparation of table comprising error patterns and syndromes
Therefore, the correct answer is A. 1, 2, 3, 4.