@inproceedings{0ae47de395a24701bd124cc76ee97a1d,
title = "On the Construction of Jointly Superregular Lower Triangular Toeplitz Matrices",
abstract = "Superregular matrices have the property that all of their submatrices, which can be full rank are so. Lower triangular superregular matrices are useful for e.g., maximum distance separable convolutional codes as well as for (sequential) network codes. In this work, we provide an explicit design for all superregular lower triangular Toeplitz matrices in GF(2p) for the case of matrices with dimensions less than or equal to 5 × 5. For higher dimensional matrices, we present a greedy algorithm that find a solution provided the field size is sufficiently high. We also introduce the notions of jointly superregular and product preserving jointly superregular matrices, and extend our explicit constructions of superregular matrices to these cases. Jointly superregular matrices are necessary to achieve optimal decoding capabilities for the case of codes with a rate lower than 1/2, and the product preserving property is necessary for optimal decoding capabilities in network recoding.",
author = "Jonas Hansen and Jan {\O}stergaard and Johnny Kudahl and John Madsen",
year = "2016",
month = jul,
doi = "https://arxiv.org/pdf/1604.07665.pdf",
language = "English",
isbn = "978-1-5090-1807-9",
series = "I E E E International Symposium on Information Theory. Proceedings",
publisher = "IEEE",
pages = "1954--1958",
booktitle = "2016 IEEE International Symposium on Information Theory (ISIT)",
address = "United States",
note = "2016 IEEE International Symposium on Information Theory, ISIT 2016, ISIT ; Conference date: 10-07-2016 Through 15-07-2016",
}