Criteria for the construction of MDS convolutional codes with good column distances
Information Theory
2023-05-26 v2 math.IT
Abstract
Maximum-distance separable (MDS) convolutional codes are characterized by the property that their free distance reaches the generalized Singleton bound. In this paper, new criteria to construct MDS convolutional codes are presented. Additionally, the obtained convolutional codes have optimal first (reverse) column distances and the criteria allow to relate the construction of MDS convolutional codes to the construction of reverse superregular Toeplitz matrices. Moreover, we present some construction examples for small code parameters over small finite fields.
Keywords
Cite
@article{arxiv.2305.04647,
title = {Criteria for the construction of MDS convolutional codes with good column distances},
author = {Zita Abreu and Julia Lieb and Raquel Pinto and Joachim Rosenthal},
journal= {arXiv preprint arXiv:2305.04647},
year = {2023}
}