Group code set is built by using a generator G of size 3 × 8 with full rank. How many distinct words can be used for communication using these code set ?
8
A group (linear) code is generated by a k × n generator matrix G of full rank k: every message word of k bits is multiplied by G to give an n-bit code word, and the set of all such products forms a subgroup of the n-bit words under addition modulo 2.
Step 1 — With G of size 3 × 8 and full rank, the message length is \(k = 3\) and the code word length is \(n = 8\).
Step 2 — Because the rank is full, distinct messages give distinct code words, so the number of usable code words equals the number of messages: \(2^{k} = 2^{3} = 8\).
The value thirty-two would be the count for five independent rows, sixteen for four rows, and four for two rows; the number of code words always depends on the number of independent rows of G, not on the code-word length.
8 option is correct.
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