Summary: We apply the well-known operator of sequences, the derivative \(D\), on codewords of linear codes. The depth of a codeword \(c\) is the smallest integer \(i\) such that \(D^ic\) (the derivative applied \(i\) consecutive times) is zero. We show that the depth distribution of the nonzero codewords of an \([n,k]\) linear code consists of exactly \(k\) nonzero values, and its generator matrix can be constructed from any \(k\) nonzero codewords with distinct depths. Interesting properties of some linear codes, and a way to partition equivalent codes into depth-equivalence classes are also discussed.