Why do linear codes claimed to be spanned by the rows of the generator matrix?
Don't they spanned by the columns of the generator matrix? i.e.
$$uG = uC_1 + \cdots u C_n = c$$
2026-04-01 20:02:29.1775073749
Why do linear codes claimed to be spanned by the rows of the generator matrix?
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If you multiply a matrix from the left (by a row vector), you obtain a row vector that is a linear combination of the row vectors of the matrix.