The depth distribution-a new characterization for linear codes

@article{Etzion1997TheDD,
title={The depth distribution-a new characterization for linear codes},
author={Tuvi Etzion},
journal={IEEE Trans. Information Theory},
year={1997},
volume={43},
pages={1361-1363}
}

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 Dc (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 exactlyk nonzero values, and its generator matrix can be constructed from anyk nonzero codewords with distinct depths. Interesting properties of some linear codes, and a way to partitionâ€¦Â CONTINUE READING