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Mathematics Coding theory Hamming weight Cryptography Hamming code Parity-check matrix Column (typography) Hamming graph Hamming distance Block code Convolutional code Linear code Coding (social sciences) Focus (optics) Algorithm Discrete mathematics Theoretical computer science Computer science Decoding methods Low-density parity-check code Statistics Connection (principal bundle) Optics Physics Geometry

Sara D. Cardell , Marcelo Firer , Diego Napp ·

YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.1109/tit.2020.2999987 · OA: W3034594523

The notion of Generalized Hamming weights of block codes has been investigated since the nineties due to its significant role in coding theory and cryptography. In this paper we extend this concept to the context of convolutional codes. In particular, we focus on column distances and introduce the novel notion of generalized column distances (GCD). We first show that the hierarchy of GCD is strictly increasing. We then provide characterizations of such distances in terms of the truncated parity-check matrix of the code, that will allow us to determine their values. Finally, the case in which the parity-check matrix is in systematic form is treated.