Group code set is built by using a generator G of size \(5 \times 8\) with full rank, then code set weight is ....................... .
At most 2
Weight of a group code = minimum weight of its non-zero code words = minimum distance \(d\).
Generator \(5 \times 8\) of full rank: \(k = 5\) message bits, \(n = 8\) code bits, \(2^5 = 32\) code words.
Hamming bound for \(d = 3\) (single error correction): \(2^k (1 + n) \le 2^n\).
\(2^5 (1 + 8) = 32 \times 9 = 288 > 2^8 = 256\), so \(d \ge 3\) is impossible.
Therefore \(d \le 2\); the values 5, 7 and 8 exceed this bound and cannot be the weight of such a code.
Hence, At most 2.
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